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RADIATION,     LIGHT    AND 
ILLUMINATION 


A   SERIES    OF   ENGINEERING    LECTURES 
DELIVERED   AT    UNION   COLLEGE 


BY 

CHARLES    PROTEUS    STEINMETZ,    A.M.,    PH.D. 

>\ 

COMPILED  AND  EDITED  BY 
JOSEPH   LEKOY   HAYDEN 


NEW   YORK 

McGRAW-HILL   BOOK    COMPANY 

239  WEST   39TH   STREET 

1909 


\  \ 


COPYRIGHT,  1909, 

BT    THE 

McGRAW-HILL  BOOK  COMPANY 
NEW  YORK 


AUTHOR'S   PREFACE. 


THE  following  lectures  were  given  as  a  course  of  instruction  to 
the  senior  students  in  electrical  engineering  at  Union  University. 

They  are  however  intended  not  merely  as  a  text-book  of 
illuminating  engineering,  nor  as  a  text-book  on  the  physics  of 
light  and  radiation,  but  rather  as  an  exposition,  to  some  extent, 
from  the  engineering  point  of  view,  of  that  knowledge  of  light 
and  radiation  which  every  educated  man  should  possess,  the 
engineer  as  well  as  the  physician  or  the  user  of  light.  For  this 
purpose  they  are  given  in  such  form  as  to  require  no  special 
knowledge  of  mathematics  or  of  engineering,  but  mathematical 
formalism  has  been  avoided  and  the  phenomena  have  been  de- 
scribed in  plain  language,  with  the  exception  of  Lectures  X  and 
XI,  which  by  their  nature  are  somewhat  mathematical,  and  are 
intended  more  particularly  for  the  illuminating  engineer,  but 
which  the  general  reader  may  safely  omit  or  merely  peruse  the 
text. 

The  lectures  have  been  revised  to  date  before  publication,  and 
the  important  results  of  the  work  of  the  National  Bureau  of 
Standards,  contained  in  its  recent  bulletins,  fully  utilized. 

CHARLES  PROTEUS  STEINMETZ. 

SCHENECTADY,  September,  1909. 


iii 


COMPILER'S  PREFACE. 


A  SERIES  of  eight  experimental  lectures  on  "  Light  and  Radia- 
tion" were  delivered  by  Dr.  Steinmetz  in  the  winter  of  1907-8 
before  the  Brooklyn  Polytechnic  Institute.  Unfortunately  no 
stenographer  was  present  and  no  manuscript  prepared  by  the 
lecturer.  A  far  more  extended  course  of  experimental  lectures 
was  however  given  by  Dr.  Steinmetz  at  Union  University  in  the 
winter  of  1908-9,  on  "  Radiation,  Light,  Illumination  and  Illu- 
minating Engineering,"  and  has  been  compiled  and  edited  in 
the  following. 

Two  additional  lectures  have  been  added  thereto  by  Dr.  Stein- 
metz to  make  the  treatment  of  the  subject  complete  even  from 
the  theoretical  side  of  illuminating  engineering :  Lecture  X  on 
"Light  Flux  and  Distribution"  and  Lecture  XI  on  "Light 
Intensity  and  Illumination."  These  two  lectures  give  the 
elements  of  the  mathematical  theory  of  illuminating  engineering. 

With  the  exception  of  the  latter  two  lectures  the  following 
book  contains  practically  no  mathematics,  but  discusses  the 
subjects  in  plain  and  generally  understood  language. 

The  subject  matter  of  Lecture  XII  on  "Illumination  and 
Illuminating  Engineering"  has  been  given  in  a  paper  before  the 
Illuminating  Engineering  Society;  the  other  lectures  are  new 
in  their  form  and,  as  I  believe,  to  a  considerable  extent  also  in 
their  contents. 

In  describing  the  experiments,  numerical  and  dimensional 
data  on  the  apparatus  have  been  given,  and  the  illustrations 
drawn  to  scale,  as  far  as  possible,  so  as  to  make  the  repetition 
of  the  experiments  convenient  for  the  reader  or  lecturer. 

Great  thanks  are  due  to  the  technical  staff  of  the  McGraw-Hill 
Book  Company,  which  has  spared  no  effort  to  produce  the  book 
in  as  perfect  a  manner  as  possible. 

JOSEPH  L.  R.  HAYDEN. 

SCHENECTADY,  September,  1909. 


CONTENTS. 


LECTURE  I.     NATURE  AND  DIFFERENT  FORMS  OF  RADIATION. 

1.  Radiation  as  energy.  j 

2.  Measurement  of  the  velocity  of  light.  2 

3.  Nature  of  light.  4 

4.  Difference  of  wave  length  with  differences  of  color.  Meas- 

urement of  wave  length  and  of  frequency.     Iridescence. 
The  ether.  6 

5.  Polarization  proving  light  a  transversal  vibration.     Double 

refraction.  7 

6.  The  visible  octave  of  radiation.     Ultra-red  and  ultra-violet 

radiation.  9 

7.  The  electric  waves.  15 

8.  The  spectrum  of  radiation  covering  60  octaves.  16 


LECTURE  II.     RELATION  OF  BODIES  TO  RADIATION. 

9.  Electric  waves  of  single  frequency,  light  waves  of  mixed 

frequency.  20 

10.  Resolving  mixed  waves  into  spectrum.     Refraction.  21 

11.  Relation  of  refractive  index  to  permeability  and  dielectric 

constant.  24 

12.  Spectrum.  25 

13.  Continuous  spectrum.     Line  spectrum.     Band  spectrum. 

Combination  spectra.  26 

14.  Reflection,  absorption  and  transmission.  29 

15.  Conversion  of  absorbed  radiation  into  heat  and  light.  30 

16.  Transmitted  light.  31 

17.  Opaque  colors  and  transparent  colors.  32 

18.  Objective  color  and  subjective  color.  33 

19.  Effect  of  excess  and  of  deficiency  of  certain  wave  length 

of  the  illuminant  on  the  opaque  and  the  transparent 
colors. 

vii 


viii  CONTENTS. 

PAGE 

LECTURE  III.     PHYSIOLOGICAL  EFFECTS  OF  RADIATION. 

Visibility. 

20.  The  eye.  37 

21.  Dependence  of  sensitivity  of  the  eye  on  the  color.     Mechan- 

ical equivalent  of  light.     Comparison  of  intensities  of 

different  colors.  40 

22.  Sensitivity  curves  of  eye  for  different  intensities.  43 

23.  Change  of  shape  of  sensitivity  curve  with  intensity.  45 

24.  Harmful  effect  of  excessive  radiation  power.  48 

25.  Protective  action  of  eye.  50 

26.  Specific  high  frequency  effect  beginning  in  blue.  51 

27.  Perception  of  ultra-violet  light.     Harmful  effects  of  ultra- 

violet. 52 

28.  Arcs  as  producers  of  ultra-violet  rays.  55 

Pathological  and  Therapeutic  Effects  of  Radiation. 

29.  Power  effect  and  specific  high  frequency  effect.  57 

30.  Light  as  germicide  and  disinfectant.  59 

LECTURE  IV.     CHEMICAL  AND  PHYSICAL  EFFECTS  OF  RADIATION. 
Chemical  Effects. 

31.  Indirect  chemical  action  by  energy  of  radiation.     Direct 

chemical  action.  63 

32.  Chemical  action  of  red  and  yellow  rays  in  supplying  the 

energy  of  plant  life.    Destructive  action  of  high  frequency 

on  plant  life.  64 

Physical  Effects. 

33.  Fluorescence  and  phosphorescence.  66 

LECTURE  V.    TEMPERATURE  RADIATION. 

34.  Production  of  radiation  by  heat.  70 

35.  Increase  of  intensity  and  frequency  with  temperature.  73 

36.  Efficiency  and  temperature.  76 

37.  Carbon  incandescent  lamp.  78 

38.  Evaporation  below  boiling  point.     Allotropic  modifications 

of  carbon.  81 

39.  Normal  temperature  radiation.  84 

40.  Colored  body  radiation.  85 

41.  Measurement  of  temperatures  by  radiation.  89 

42.  Colored  radiation  and  heat  luminescence.  90 


CONTENTS.  ix 

PAGE 

LECTURE  VI.     LUMINESCENCE. 
Fluorescence  and  Phorphorescence. 

43.  Radioluminescence.       Electroluminescence.      Thermolumi- 

nescence.     Physical    phosphorescence.      Chemical  phos- 
phorescence.    Biological  phosphorescence.  94 

44.  Pyroluminescence.     Chemical  luminescence.  96 

45.  Electroluminescence  of  gases  and  vapors.  98 

Disruptive  Conduction. 

46.  Geissler  tube  and  spark.     Disruptive  voltage.  101 

47.  Change  from  spark  to  Geissler  glow.  105 

Continuous  Conduction. 

48.  Nature  of  continuous  or  arc  conduction.  106 

49.  Distinction  between  arc  and  spark  discharge.  Ill 

50.  Continuity  at  negative.  113 

51.  Rectification  of  alternating  voltages  by  arcs.  117 

52.  Efficiency  and  color.  122 

53.  Most  efficient  light  producer.  123 

54.  Electro-conduction  from  negative,  long  life,  non-consuming 

positive,  limitation  in  the  available  materials.  125 

55.  Arc  most  efficient  method  of  light  production.  126 

LECTURE  VII.     FLAMES  AS  ILLUMINANTS. 

56.  Hydrocarbon  flames.  128 

57.  Effect  of  rapidity  of  combustion  and  of  flame  shape  on 

smokiness.  130 

58.  Effect  of  oxygen  atom  in  the  hydrocarbon  molecule   on 

luminosity.  132 

59.  Mixture  of  hydrocarbon  with  air.  133 

60.  Chemical  luminescence.  134 

61.  Flames  with  separate  radiator.  135 

LECTURE  VIII.     ARC  LAMPS  AND  ARC  LIGHTING. 
Volt- Ampere  Characteristics  of  the  Arc. 

62.  Arc  length  and  voltage.  137 

63.  General  equations  of  the  arc.  140 
Stability  Curves  of  the  Arc. 

64.  Instability  on  constant  voltage..  142 

65.  Equations  of  the  vapor  arc.  145 
Arc  Length  and  Efficiency. 

66.  Maximum  efficiency  length  of  carbon  arc.  146 

67.  Maximum  efficiency  length  of  luminous  arc.  148 


X  CONTENTS. 

PAGE 

LECTURE  VIII.     ARC  LAMPS  AND  ARC  LIGHTING  (Continued). 
Arc  Lamps. 

68.  The  elements  of  the  arc  lamp.  151 

69.  Differential  arc  lamp.  153 

70.  Series  arc  lamp.  157 

71.  Luminous  arc  lamp.  160 

Arc  Circuits. 

72.  Constant  potential  and   constant   current.     The   mercury 

arc  rectifier  system.     The  arc  machine.  160 

73.  The  constant  current  transformer.     The  constant  current 

reactance.  163 

LECTURE  IX.     MEASUREMENT  OF  LIGHT  AND  RADIATION. 

74.  Measurement  of  radiation  as  power.  166 

75.  Light  a  physiological  quantity.  167 

76.  Physiological  feature  involved  in  all  photometric  methods.  169 

77.  Zero  method  photometers.  170 

78.  Comparison  of  lights.  172 

79.  Flicker  photometer.  173 

80.  The  luminometer.  175 

81.  Primary  standards  of  light.  177 

82.  Proposed  primary  standards.  178 

83.  Illumination  and  total  flux  of  light.     Incandescent  lamp 

photometry.  179 

84.  Arc  lamp  photometry.  182 

85.  Discussion.     Mean  spherical,  horizontal,  downwards,  maxi- 

mum, hemispherical  candle  power.  184 

LECTURE  X.     LIGHT  FLUX  AND  DISTRIBUTION. 

86.  Light  flux,  light  flux  density,  light  intensity.  186 

87.  Symmetrical  and  approximately  symmetrical  distribution.  187 

88.  Calculation  of  light  flux  from  meridian  curve  of  symmetri- 

cal radiator.  188 

Distribution  Curves  of  Radiation. 

89.  Calculation   of  distribution  curves.     Point  or  sphere   of 

uniform  brilliancy.  190 

90.  Straight  line  or  cylindrical  radiator.  195 

91.  Circular  line  or  cylinder.  197 

92.  Single  loop  filament  incandescent  lamp  as  illustration.  200 


CONTENTS.  xi 

PAGE 

LECTURE  X.     LIGHT  FLUX  AND  DISTRIBUTION  (Continued). 
Shadows. 

93.  Circular  shade  opposite  and  symmetrical  to  circular  radia- 

tor. 202 

94.  Calculation  of  the  meridian  curves  of  a  circular  radiator,  for 

different  sizes  of  a  symmetrical  circular  shade,  and  for 
different  distances  of  it.  206 

95.  Circular  shade  concentric  with  end  of  linear  radiator.  210 

Reflection. 

96.  Irregular  reflection.  212 

97.  Regular  reflection.  215 

98.  Reflector  with  regular  and  irregular  reflection.  218 

Diffraction,  Diffusion  and  Refraction. 

99.  Purpose  of  reducing  the  brilliancy  of  the  illuminant.  221 

100.  Effect  of  the  shape  of  the  diffusing  globe  on  the  distribu- 

tion curve.  223 

101.  Prismatic  refraction  and  reflection.  224 


LECTURE  XI.     LIGHT  INTENSITY  AND  ILLUMINATION. 

Intensity  Curves  for  Uniform  Illumination. 

102.  Calculation  of    intensity  distribution  of    illuminant  for 

uniform  total,  horizontal  and  vertical  illumination.  226 

103.  Uniform  illumination  of  limited  area.  229 

Street  Illumination  by  Arcs. 

104.  Discussion  of  problem.  234 

105.  Combined  effect  of  successive  lamps. 

Room  Illumination  by  Incandescent  Lamps. 

106.  Distribution  curve  of  lamp.     Calculation  of  resultant  total 

intensity  of  direct  light. 

107.  Reflection  from  walls  and  ceiling.  246 

108.  Total  directed  and  diffused  illumination.  251 

Horizontal  Table  Illumination  by  Incandescent  Lamps. 

109.  Location  of  lamps.  253 


xii  CONTENTS. 

PAGE 

LECTURE  XII.     ILLUMINATION  AND  ILLUMINATING  ENGINEERING. 

110.  Physical  and  physiological  considerations.  256 

111.  Light  flux  density.     Illumination.     Brilliancy.  259 

112.  Physical  problems.    Ceilings  and  walls.    Reflectors,  diffus- 

ing globes,  diffracting  shades,  etc.  260 

113.  Objective    illumination.     Subjective    illumination.     Con- 

traction of  pupil.     Intrinsic  brilliancy.     Direct  and  in- 
direct lighting.  261 

114.  Fatigue.  263 

115.  Differences  in  intensity  and  in  color.     Control  of  color 

differences.     Shadows  and  their  control.     Directed  and 
diffused  light.  265 

116.  Direction  of  shadows.  267 

117.  Color  sensitivity  in  relation  to  required  intensity  of  illu- 

mination. 269 

118.  Domestic  lighting.  270 

119.  The  twofold  problem  of  domestic  lighting:  daylight  and 

artificial  light.  271 

120.  Street  lighting.  272 

121.  Defects  of  present  street  lighting.                                             273 

122.  Tower  lighting.  274 

LECTURE   XIII.  —  PHYSIOLOGICAL    PROBLEMS    OF    ILLUMINATING 
ENGINEERING. 

123.  Physical  side  of  illuminating  engineering.     Physiological 

problems.  277 

124.  Physiological   difference   between   diffused  and   directed 

light.  278 

125.  Indefmiteness  of  diffused  light.     Shadows  cast  by  diffused 

daylight.     Equivalent   diffusion   near  light   source   of 
large  extent.  279 

126.  Equivalent  diffusion  by  using  several  light  sources.  281 

127.  Unequal     diffusion     in     different     directions.     Complex 

shadows.  282 

128.  Physiological  light  distribution.  283 

129.  Physiologically,  light  not  a  vector  quantity.  284 

130.  Resultant  effect  of  several  light  sources.  287 


RADIATION,  LIGHT,  AND 
ILLUMINATION. 


LECTURE  I. 
NATURE    AND    DIFFERENT    FORMS    OF    RADIATION. 

1.  Radiation  is  a  form  of  energy,  and,  as  such,  can  be  produced 
from  other  forms  of  energy  and  converted  into  other  forms  of 
energy. 

The  most  convenient  form  of  energy  for  the  production  of  rad- 
iation is  heat  energy,  and  radiation  when  destroyed  by  being 
intercepted  by  an  opaque  body,  usuaDy  is  converted  into  heat. 
Thus  in  an  incandescent  lamp,  the  heat  energy  produced  by  the 
electric  current  in  the  resistance  of  the  filament,  is  converted 
into  radiation.  If  I  hold  my  hand  near  the  lamp,  the  radiation 
intercepted  by  the  hand  is  destroyed,  that  is,  converted  into  heat, 
and  is  felt  as  such.  On  the  way  from  the  lamp  to  the  hand,  how- 
ever, the  energy  is  not  heat  but  radiation,  and  a  body  which  is 
transparent  to  the  radiation  may  be  interposed  between  the 
lamp  and  the  hand  and  remains  perfectly  cold.  The  terms 
"heat  radiation "  and  " radiant  heat,"  which  are  occasionally 
used,  therefore  are  wrong:  the  so-called  radiant  heat  is  not  heat 
but  radiation  energy,  and  becomes  heat  only  when,  intercepted 
by  an  opaque  body,  it  ceases  to  be  radiation;  the  same,  however, 
applies  to  any  radiation.  If  we  do  not  feel  the  radiation  of  a 
mercury  lamp  or  that  of  the  moon  as  heat,  while  we  feel  that  of  a 
coal  fire,  it  is  merely  because  the  total  energy  of  the  latter  is  very 
much  greater;  a  sufficiently  sensitive  heat-measuring  instrument, 
as  a  bolometer,  shows  the  heat  produced  by  the  interception  of 
the  rays  of  the  mercury  lamp  or  the  rays  of  the  moon. 

The  most  conspicuous  form  of  radiation  is  light,  and,  therefore, 
it  was  in  connection  with  this  form  that  the  laws  of  radiation 
were  first  studied. 

1 


2  RADIATION,  LIGHT,  AND  ILLUMINATION. 

2.  The  first  calculations  of  the  velocity  of  light  were  made  by 
astronomers  in  the  middle  of  the  eighteenth  century,  from  the 
observations  of  the  eclipses  of  the  moons  of  Jupiter.  A  number 
of  moons  revolve  around  the  planet  Jupiter,  some  of  them  so  close 
that  seen  from  the  earth  they  pass  behind  Jupiter  and  so  are 
eclipsed  at  every  revolution.  As  the  orbits  of  Jupiter's  moons 
were  calculated  from  their  observations  by  the  law  of  gravita- 
tion, the  time  at  which  the  moon  M  should  disappear  from  sight, 


FIG.  1. 

when  seen  from  the  earth  E,  by  passing  behind  Jupiter,  7  (Fig.  1), 
could  be  exactly  calculated.  It  was  found,  however,  that  some- 
times the  moon  disappeared  earlier,  sometimes  later  than  cal- 
culated, and  the  difference  between  earliest  and  latest  disappear- 
ance amounts  to  about  17  min.  It  was  also  found  that  the 
disappearance  of  the  moon  behind  Jupiter  occurred  earlier  when 
the  earth  was  at  the  same  side  of  the  sun  as  Jupiter,  at  A,  while 
the  latest  disappearance  occurred  when  the  earth  was  on  the 
opposite  side  of  the  sun  from  Jupiter,  at  B.  Now,  in  the  latter 
case,  the  earth  is  further  distant  from  Jupiter  by  the  diameter 
ASB  of  the  orbit  of  the  earth  around  the  sun  S,  or  by  about 
195,000,000  miles  and  the  delay  of  17J  min.  thus  must  be  due  to 
the  time  taken  by  the  light  to  traverse  the  additional  distance 
of  195,000,000  miles.  Seventeen  and  one-third  min.  are  1040 
sec.  and  195,000,000  miles  in  1040  sec.  thus  gives  a  velocity  of 


light  of  »  or  188,000  miles  per  sec. 


Later,  the  velocity  of  light  was  measured  directly  in  a  number 
of  different  ways.  For  instance,  let,  in  Fig.  2,  D  be  a  disk  per- 
forated with  holes  at  its  periphery.  A  lamp  L  sends  its  light 
through  a  hole  H0  in  the  disk  to  a  mirror  M  located  at  a  con- 
siderable distance,  for  instance  5  miles;  there  the  light  is  reflected 


NATURE  AND  DIFFERENT  FORMS  OF  RADIATION.      3 

and  the  mirror  is  adjusted  so  that  the  reflected  beam  of  light 
passes  through  another  hole  Hl  of  the  disk  into  the  telescope  T. 
If  the  disk  is  turned  half  the  pitch  of  the  holes  the  light  is  blotted 
out  as  a  tooth  stands  in  front  of  both  the  lamp  and  the  telescope. 
Again  turning  the  disk  half  the  pitch  of  the  holes  in  the  same 


5_MOE_S 


FIG.  2. 

direction  the  light  reappears.  If  the  disk  is  slowly  revolved,  alter- 
nate light  and  darkness  will  be  observed,  but  when  the  speed  in- 
creases so  that  more  than  from  10  to  20  holes  pass  per  second,  the 
eye  is  no  longer  able  to  distinguish  the  individual  flashes  of  light 
but  sees  a  steady  and  uniform  light;  then  increasing  the  speed 
still  more  the  light  grows  fainter  and  finally  entirely  disappears. 
This  means  when  a  hole  H0  is  in  front  of  the  lamp,  a  beam  of 
light  passes  through  the  hole.  During  the  time  taken  by  the  light 
to  travel  the  10  miles  to  the  mirror  and  back,  the  disk  D  has 
moved,  and  the  hole  Hv  which  was  in  front  of  the  telescope 
when  the  light  from  the  lamp  passed  through  the  hole  HQ,  has 
moved  away,  and  a  tooth  is  now  in  front  of  the  telescope  and 
intercepts  the  light.  Therefore,  at  the  speed  at  which  the  light 
disappears,  the  time  it  takes  the  disk  to  move  half  the  pitch  of  a 
hole  is  equal  to  the  time  it  takes  the  light  to  travel  10  miles. 

Increasing  still  further  the  velocity  of  the  disk  D,  the  light 
appears  again,  and  increases  in  brilliancy,  reaching  a  maximum 
at  twice  the  speed  at  which  it  had  disappeared.  Then  the  light 
reflected  from  the  mirror  M  again  passes  through  the  center  of 
a  hole  into  the  telescope,  but  not  through  the  same  hole  Ht 
through  which  it  would  have  passed  with  the  disk  stationary,  but 
through  the  next  hole  H2,  that  is,  the  disk  has  moved  a  distance 
equal  to  the  pitch  of  one  hole  while  the  light  traveled  10  miles. 
Assume,  for  instance,  that  the  disk  D  has  200  holes  and  makes 


4  RADIATION,  LIGHT,  AND  ILLUMINATION. 

94  rev.  per  sec.  at  the  moment  when  the  light  has  again  reached 
full  brilliancy*  In  this  case,  200  X  94  =  18,800  holes  pass  the 
telescope  per  second,  and  the  time  of  motion  by  the  pitch  of  one 

hole  is sec.,  and  as  this  is  the  time  required  by  the  light 

18,800 

to  travel  10  miles,  this  gives  the  velocity  of  light  as  10  •*  > 

lo,oOU 

or  188,000  miles  per  sec. 

The  velocity  of  light  in  air,  or  rather  in  empty  space,  thus  is 
188,000  miles  or  3  X  1010  cm.  per  sec. 

For  electrical  radiation,  the  velocity  has  been  measured  by 
Herz,  and  found  to  be  the  same  as  the  velocity  of  light,  and  there 
is  very  good  evidence  that  all  radiations  travel  with  the  same 
velocity  through  space  (except  perhaps  the  rays  of  radioactive 
substances). 

3.  Regarding  the  nature  of  radiation,  two  theories  have  been 
proposed.  Newton  suggested  that  light  rays  consisted  of 
extremely  minute  material  particles  thrown  off  by  the  light- 
giving  bodies  with  enormous  velocities,  that  is,  a  kind  of  bom- 
bardment. This  theory  has  been  revived  in  recent  years  to 
explain  the  radiations  of  radium,  etc.  Euler  explained  the  light 
as  a  wave  motion.  Which  of  these  explanations  is  correct 
can  be  experimentally  decided  in  the  following  manner:  Assum- 
ing light  to  be  a  bombardment  of  minute  particles,  if  we  com- 
bine two  rays  of  light  in  the  same  path  they  must  add  to  each 
other,  that  is,  two  equal  beams  of  light  together  give  a  beam  of 
twice  the  intensity.  If,  however,  we  assume  light  is  a  wave 
motion,  then  two  equal  beams  of  light  add  to  one  of  twice  the 
intensity  only  in  case  the  waves  are  in  phase,  as  Al  and  B^  in 
Fig.  3  add  to  Cr  If,  however,  the  two  beams  A2  and  B2  are  not 
in  phase,  their  resultant  C2  is  less  than  their  sum,  and  if  the 
two  beams  A3  and  B3  in  Fig.  3  happen  to  be  in  opposition 
(180  degrees  apart),  that  is,  one-half  wave  length  out  of  phase 
with  each  other,  their  resultant  is  zero,  that  is,  they  blot  each 
other  out. 

Assuming  now  we  take  a  plain  glass  plate  A  (Fig.  4)  and  a 
slightly  curved  plate  B,  touching  each  other  at  (7,  and  illuminate 
them  by  a  beam  of  uniform  light  —  as  the  yellow  light  given  by 
coloring  the  flame  of  a  bunsen  burner  with  some  sodium  salt  — 
a  part  of  the  light  b,  is  then  reflected  from  the  lower  surface  of 


NATURE  AND  DIFFERENT  FORMS  OF  RADIATION.      5 

the  curved  glass  plate  B,  a  part  c,  passes  out  of  it,  and  is  reflected 
from  the  upper  surface  of  the  plain  glass  plate  A.    A  beam  of 


FIG.  3. 


reflected  light  a,  thus  is  a  combination  of  a  beam  b  and  a  beam  c. 
The  two  beams  of  light  which  combine  to  a  single  one,  a,  differ 
from  each  other  in  phase  by  twice  the  distance  between  the  two 
glass  plates.  At  those  points  dv  dv  etc.  at  which  the  distance 


FIG.  4. 


between  the  two  glass  plates  is  J  wave  length,  or  j,  J,  etc.,  the 
two  component  beams  of  a  would  differ  by  \,  f ,  |,  etc.  wave 
lengths,  and  thus  would  blot  each  other  out,  producing  darkness, 


6  RADIATION,  LIGHT,  AND  ILLUMINATION. 

while  at  those  points  where  the  distance  between  the  glass  plates 
is  J,  1,  lj,  etc.  wave  lengths,  and  the  two  component  beams  a 
thus  differ  in  phase  by  a  full  wave  or  a  multiple  thereof,  they 
would  add.  If,  therefore,  light  is  a  wave  motion,  such  a  structure 
would  show  the  contact  point  C  of  the  plates  surrounded  by 
alternate  dark  rings,  d,  and  bright  rings,  y.  This  is  actually  the 
case,  and  therefore  this  phenomenon,  called  " interference" 
proves  light  to  be  a  wave  motion,  and  has  lead  to  the  universal 
acceptance  of  the  Eulerian  theory. 

Measuring  the  curvature  of  the  plate  B,  and  the  diameter 
of  the  dark  rings  d,  the  distance  between  the  plates  B  and  A  at 
the  dark  rings  d,  can  be  calculated  and  as  this  distance  is  one- 
quarter  wave  length,  or  an  odd  multiple  thereof,  the  wave 
length  can  be  determined  therefrom. 

The  wave  length  of  light  can  be  measured  with  extremely  high 
accuracy  and  has  been  proposed  as  the  absolute  standard  of 
length,  instead  of  the  meter,  which  was  intended  to  be  10~7  of 
the  quadrant  of  the  earth. 

4.  It  is  found,  however,  that  the  different  colors  of  light  have 
different  wave  lengths;  red  light  has  the  greatest  wave  length, 
and  then  in  the  following  order:  red,  orange,  yellow,  green,  blue, 
indigo,  violet,  the  wave  length  decreases,  violet  light  having  the 
shortest  wave  length. 

If  in  experiment  (Fig.  4)  instead  of  uniform  light  (monochro- 
matic light),  ordinary  white  light  is  used,  which  is  a  mixture  of 
all  colors,  the  dark  and  bright  rings  of  the  different  colors  appear 
at  different  distances  from  each  other,  those  of  the  violet  near- 
est and  those  of  the  red  the  furthest  apart,  and  so  superimpose 
upon  each  other,  and  instead  of  alternately  black  and  light  rings, 
colored  rings  appear,  so-called  interference  rings.  Wherever  a 
thin  film  of  air  or  anything  else  of  unequal  thickness  is  inter- 
posed between  two  other  materials,  such  interference  colors  thus 
appear.  They  show,  for  instance,  between  sheets  of  mica,  etc. 
The  colors  of  soap  bubbles  are  thus  produced. 

The  production  of  such  colors  by  the  interference  of  rays  of 
light  differing  from  each  other  by  a  fractional  wave  length  is 
called  iridescence. 

Iridescent  colors,  for  instance,  are  those  of  mother-of-pearl, 
of  opal,  of  many  butterflies,  etc. 

Light,  therefore,  is  a  wave  motion. 


NATURE  AND  DIFFERENT  FORMS  OF  RADIATION.      1 

The  frequency  of  radiation  follows  from  the  velocity  of  light, 
and  the  wave  length. 

The  average  wave  length  of  visible  radiation,  or  light,  is  about 
lw  =  60  microcentimeters,*  that  is,  60  X  10~8  cm.  (or  about 
^<y^<5-<y  in.)  and  since  the  speed  is  S  =  3  X  1010  cm.  the  frequency 

a 

is  /  =  r-  =  500  X  1012,  or  500  millions  of  millions  of  cycles  per 

LW 

second,  that  is,  inconceivably  high  compared  with  the  frequencies 
with  which  we  are  familiar  in  alternating  currents. 

If,  as  proven,  light  is  a  wave  motion,  there  must  be  some  thing 
which  is  moving,  a  medium, 'and  from  the  nature  of  the  wave 
motion,  its  extremely  high  velocity,  follow  the  properties  of  this 
medium:  it  has  an  extremely  high  elasticity  and  extremely  low 
density,  and  it  must  penetrate  all  substances  since  no  vacuum  can 
be  produced  for  this  medium,  because  light  passes  through  any 
vacuum.  Hence  it  cannot  be  any  known  gas,  but  must  be  essen- 
tially different,  and  has  been  called  the  "ether." 

Whether  the  ether  is  a  form  of  matter  or  not  depends  upon 
the  definition  of  matter.  If  matter  is  defined  as  the  (hypotheti- 
cal) carrier  of  energy  (and  all  the  information  we  have  of  matter 
is  that  it  is  the  seat  of  energy) ,  then  the  ether  is  matter,  as  it  is  a 
carrier  of  energy:  the  energy  of  radiation,  during  the  time  be- 
tween the  moment  when  the  wave  leaves  the  radiator  and  the 
moment  when  it  strikes  a  body  and  is  absorbed,  resides  in  the 
ether. 

5.  If  light  is  a  wave  motion  or  vibration,  it  may  be  a  longitudi- 
nal vibration,  or  a  transversal  vibration;  that  is,  the  particles  of 
the  medium  which  transmit  the  vibrations  may  move  in  the 
direction  in  which  the  wave  travels,  as  is  the  case  with  sound 
waves  in  air.  If  in  Fig.  5  sound  waves  travel  from  the  bell  B  in 
the  direction  BA,  the  air  molecules m  vibrate  in  the  same  direction, 
A  to  B.  Or  the  vibration  may  be  transversal ;  that  is,  if  the  beam 

*  As  measures  of  the  wave  length  of  light,  a  number  of  metric  units  have 
survived  and  are  liable  to  lead  to  confusion: 

The  micron,  denoted  by  ft,  equal  to  one  thousandth  of  a  millimeter. 

The  fJLfJ.,  equal  to  one  millionth  of  a  millimeter. 

The  Angstrom  unit,  equal  to  one  ten-millionth  of  a  millimeter. 

As  seen,  the  basis  of  these  units  is  the  millimeter,  which  was  temporarily 
used  as  a  standard  unit  of  length  before  the  establishment  of  the  present 
absolute  system  of  units,  the  (C.G.S),  which  is  based  on  centimeter  length, 
gram  mass,  and  second  time  measure. 

A  radiation  of  the  wave  length  of  60  microcentimeters  thus  can  be  expressed 
also  as:  6000  Angstrom  units,  or  0.6  p,  or  600  pp. 


8  RADIATION,  LIGHT,  AND  ILLUMINATION. 

of  light  moves  in  Fig.  6  perpendicularly  to  the  plane  of  the  paper, 
the  vibrating  particles  move  in  any  one  of  the  directions  oa,  ob, 
etc.  in  the  plane  of  the  paper,  and  thus  perpendicular  to  the  ray 


FIG.  5. 

of  light.  In  the  former  case  (a  longitudinal  vibration,  as  sound) 
there  obviously  can  be  no  difference  between  the  directions  at 
right  angles  to  the  motion  of  the  wave.  In  a  transversal  vibra- 
tion, however,  the  particles  may  move  either  irregularly  in  any 
of  the  infinite  number  of  directions  at  right  angles  to  the  ray 
(Fig.  6)  and  thus  no  difference  exists  in  the  different  directions 
perpendicular  to  the  beam,  or  they  may  vibrate  in  one  direction 
only,  as  the  direction  boa  (Fig.  7).  In  the  latter  case,  the  wave  is 

called  " polarized"  and  has  differ- 
ent characteristics  in  three  direc- 
tions at  right  angles  to  each  other : 
one  direction  is  the  direction  of 
propagation,  or  of  wave  travel;  the 
second  is  the  direction  of  vibration; 
IG'  6'  and  the  third  is  the  direction  per- 

pendicular to  progression  and  to  vibration.  For  instance,  the 
electric  field  of  a  conductor  carrying  alternating  current  is  a 
polarized  wave:  the  direction  parallel  to  the  conductor  is  the 
direction  of  energy  flow;  the  direction  concentric  to  the  con- 
ductor is  the  direction  of  the  electromagnetic  component,  and 
the  direction  radial  to  the  conductor  is  the  direction  of  the 
electrostatic  component  of  the  electric  field. 

Therefore,  if  light  rays  can  be  polarized,  that  is,  made  to  ex- 
hibit different  properties  in  two  directions  at  right  angles  to  each 
other  and  to  the  direction  of  wave  travel,  this  would  prove  tke 
light  wave  to  be  a  transversal  vibration.  This  is  actually  the  case. 
For  instance,  if  a  beam  of  light  is  reflected  a  number  of  times 
under  a  fairly  sharp  angle,  as  shown  in  Fig.  8,  this  beam  becomes 
polarized ;  that  is,  for  instance,  the  reflection  from  the  mirror  m0, 
set  like  the  mirrors  mv  m2  .  .  .  which  produced  the  polarization, 


NATURE  AND  DIFFERENT  FORMS  OF  RADIATION.      9 

is  greater,  and  the  absorption  less  than  from  a  mirror  set  at  right 
angles  thereto,  as  ra/. 

Some  crystals,  as  Iceland  spar  (calcium  carbonate),  show 
"double  refraction,"  that  is,  dissolve  a  beam  of  light,  a,  enter- 
ing them  into  two  separate  beams,  b  and  c  (Fig.  9)  which  are 
polarized  at  right  angles  to  each  other. 

In  a  second  crystal,  K2,  beam  b  would  then  enter  as  a  single 
beam,  under  the  same  angle  as  in  the  first  crystal  Kv  if  K2  were 
in  the  same  position  as  Kl ;  while  if  K2  were  turned  at  right  angles 
to  Kv  beam  b  would  enter  K2  under  the  same  angle  as  beam  c  in 
crystal  Kr 

6.  As  seen,  light  and  radiation  in  general  are  transversal  wave 


motions  of  very  high  speed,  S  =  3  X  1010  cm.  per  sec.  in  a  hypo- 
thetical medium,  ether,  which  must  be  assumed -to  fill  all  space 
and  penetrate  all  substances. 

Radiation  is  visible,  as  light,  in  a  narrow  range  of  frequencies 
only:  between  400  X  1012  and  770  X  1012  cycles  per  sec.  cor- 
responding to  wave  lengths  from  76  X  10"6  cm.  to  39  X  10"'  cm.* 
All  other  radiations  are  invisible  and  thus  have  to  be  observed  by 
other  means. 

I  have  here  a  pair  of  rods  of  cast  silicon  (10  in.  long,  0.22  in.  in 
diameter,  having  a  resistance  of  about  10  ohms  each),  connected 

*  The  visibility  of  radiation  is  greatest  between  the  wave  lengths  50  X  10~* 
to  60  X  10~e  and  good  between  the  wave  lengths  41  X  10~e  to  76  X  10~8, 
but  extends  more  or  less  indistinctly  over  the  range  of  wave  lengths  from 
33  X  10~6  to  77  X  10~6  and  faintly  even  as  far  as  30  X  10~fl  to  100  X 


10 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


in  series  with  each  other  and  with  a  rheostat  of  about  40  ohms 
resistance  in  a  120-volt  circuit.  When  I  establish  a  current 
through  the  rods,  electric  energy  is  converted  into  heat  by  the 
resistance  of  the  rods.  This  heat  energy  is  converted  into  and 
sent  out  as  radiation,  with  the  exception  of  the  part  carried  off 
by  heat  conduction  and  convection.  Reducing  the  resistance,  I 
increase  the  heat,  and  thereby  the  radiation  from  the  silicon  rods. 
Still  nothing  is  visible  even  in  the  dark;  these  radiations  are  of 
too  low  frequency,  or  great  wave  length,  to  be  visible.  By  hold- 
ing my  hand  near  the  rods,  I  can  feel  the  energy  as  heat,  and  show 
it  to  you, by  bringing  the  rods  near  to  this  Crookes'  radiometer, 


FIG.  9. 

which  is  an  instrument  showing  the  energy  of  radiation.  It  con- 
sists (Fig.  10)  of  four  aluminum  vanes,  mounted  in  a  moderately 
high  vacuum  so  that  they  can  move  very  easily.  One  side  of  each 
vane  is  polished,  the  other  blackened.  The  waves  of  radiation 
are  reflected  on  the  polished  side  of  the  vane;  on  the  blackened 
side  they  are  absorbed,  produce  heat,  thus  raise  the  temperature  of 
the  air  near  the  vane;  the  air  expands  and  pushes  the  vanes  ahead, 
that  is,  rotates  the  wheel.  As  you  see,  when  I  bring  the  heated 
rods  near  the  radiometer,  the  wheel  spins  around  at  a  rapid  rate 
by  the  radiation  from  the  rods,  which  to  the  eye  are  invisible. 


NATURE  AND  DIFFERENT  FORMS  OF  RADIATION.    11 


Increasing  still  further  the  energy  input  into  the  silicon  rods,  and 
thereby  their  temperature,  the  intensity  of  radiation  increases, 
'but  at  the  same  time  radiations  of  higher  and  higher  frequencies 
appear,  and  ultimately  the  rods  become  visible  in  the  dark, 
giving  a  dark  red  light;  that  is,  of  all  the  radiations  sent  out  by 
the  rods,  a  small  part  is  of  sufficiently  high  frequency  to  be  visible. 
Still  further  increasing  the  tempera- 
ture, the  total  radiation  increases, 
but  the  waves  of  high  frequency  in- 
crease more  rapidly  than  those  vof 
lower  frequency ;  that  is,  the  average 
frequency  of  radiation  increases  or 
the  average  wave  length  decreases 
and  higher  and  higher  frequencies 
appear, — orange  rays,  yellow,  green, 
blue,  violet,  and  the  color  of  the 
light  thus  gradually  changes  to 
bright  red,  orange,  yellow.  Now  I 
change  over  from  the  silicon  rods  — 
which  are  near  the  maximum  tem- 
perature they  can  stand  —  to  a  tung- 
sten lamp  (a  40- watt  110- volt  lamp, 
connected  in  series  with  a  rheostat 
of  2000  ohms  resistance  in  a  240- 
volt  circuit).  For  comparison  I  also 
turn  on  an  ordinary  16  c.  p.  carbon 
filament  incandescent  lamp,  running 
at  normal  voltage  and  giving  its 
usual  yellow  light.  Gradually  turn- 
ing out  the  resistance,  the  light  of 
the  tungsten  lamp  changes  from 
orange  to  yellow,  yellowish  white 
and  ultimately,  with  all  the  resistance  cut  out  and  the  fila- 
ment running  at  more  than  double  voltage,  is  practically  white; 
that  is,  gives  a  radiation  containing  all  the  frequencies  of  visible 
light  in  nearly  the  same  proportion  as  exist  in  sunlight.  If  we 
should  go  still  further  and  very  greatly  increase  the  temperature, 
probably  because  of  the  more  rapid  increase  of  the  higher  fre- 
quencies (violet,  blue,  green)  than  the  lower  frequencies  of  light 
(red,  orange  and  yellow)  with  increase  in  temperature,  the  light 


FIG.  10. 


12 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


would  become  bluish.  However,  we  are  close  to  the  limit  of 
temperature  which  even  tungsten  can  stand,  and  to  show  you 
light  of  high  frequency  or  short  wave  length  I  use  a  different 
apparatus  in  which  a  more  direct  conversion  of  electric  energy 
into  radiation  takes  place,  —  the  mercury  arc  lamp.  Here  the 
light  is  bluish  green,  containing  only  the  highest  frequencies 
of  visible  radiation,  violet,  blue  and  green,  but  practically  none 
of  the  lower  frequencies  of  visible  radiation,  red  or  orange. 


FIG.  11. 


In  the  tungsten  lamp  at  high  brilliancy  and  more  still  in  the 
mercury  arc,  radiations  of  higher  frequencies  appear,  that  is, 
shorter  wave  lengths  than  visible  light,  and  these  radiations  are 
again  invisible.  As  they  are  of  frequencies  beyond  the  violet 
rays  of  light,  they  are  called  " ultra-violet  rays/'  while  the  radia- 
tions which  we  produced  from  the  heated  silicon  rods  at  moderate 
temperatures  were  invisible  because  of  too  low  frequency  and 
are  thus  called  "  ultra-red  rays,"  or  " infra-red  rays/'  as  they  are 
outside  of  and  below  the  red  end  of  the  range  of  visible  radiation. 

To  produce  powerful  ultra-violet  rays,  I  use  a  condenser  dis- 
charge between  iron  terminals,  a  so-called  ultra-violet  arc  lamp. 
Three  iron  spheres,  7  in  Fig.  11,  of  about  f  in.  diameter,  are 
mounted  on  an  insulator  B.  The  middle  sphere  is  fixed,  the 


NATURE  AND  DIFFERENT  FORMS  OF  RADIATION.    13 

outer  ones  adjustable  and  set  for  about  ^  in.  gap.  This  lamp  is 
connected  across  a  high  voltage  0.2-mf.  mica  condenser  C,  which 
is  connected  to  the  high  voltage  terminal  of  a  small  step-up  trans- 
former T  giving  about  15,000  volts  (200  watts,  110  •*-  13,200 
volts).  The  low  tension  side  of  the  transformer  is  connected  to 
the  240-volt  60-cycle  circuit  through  a  rheostat  R  to  limit  the 
current.  The  transformer  charges  the  condenser,  and  when  the 
voltage  of  the  condenser  has  risen  sufficiently  high  it  discharges 
through  the  spark  gaps  I  by  an  oscillation  of  high  frequency 
(about  500,000  cycles),  then  charges  again  from  the  transformer, 
discharges  through  the  gap,  etc.  As  several  such  condenser  dis- 
charges occur  during  each  half  wave  of  alternating  supply  voltage 
the  light  given  by  the  discharge  appears  continuous. 

You  see,  however,  that  this  iron  arc  gives  apparently  very  little 
light;  most  of  the  radiation  is  ultra-violet,  that  is,  invisible  to  the 
eye.  To  make  it  visible,  we  use  what  may  be  called  a  frequency 
converter  of  radiation.  I  have  here  a  lump  of  willemite  (native 
zinc  silicate),  a  dull  greenish  gray  looking  stone.  I  put  it  under 
the  iron  arc  and  it  flashes  up  in  a  bright  green  glare  by  convert- 
ing the  higher  frequency  of  ultra-violet  rays  into  the  lower 
frequency  of  green  light.  This  green  light  is  not  given  by  the 
iron  arc,  as  a  piece  of  white  paper  held  under  the  arc  shows  only 
the  faint  illumination  given  by  the  small  amount  of  visible  radia- 
tion. I  now  move  a  thin  sheet  of  glass,  or  of  mica,  between  the 
iron  arc  and  the  lump  of  willemite,  and  you  see  the  green  light 
disappear  as  far  as  the  glass  casts  a  shadow.  Thus  glass  or  mica, 
while  transparent  to  visible  light,  is  opaque  for  the  ultra-violet 
light  of  the  iron  arc.  A  thick  piece  of  crystallized  gypsum  (sel- 
enite)  put  in  the  path  of  the  ultra-violet  light  does  not  stop  it, 
hence  is  transparent,  as  the  lump  of  willemite  continues  to  show 
the  green  light,  or  a  piece  of  cast  glass  its  blue  light. 

I  have  here  some  pieces  of  willemite  in  a  glass  test  tube.  They 
appear  dull  and  colorless  in  the  ultra-violet  light,  as  the  glass  is 
opaque  for  this  light.  I  shift  them  over  into  a  test  tube  of  fused 
quartz,  and  you  see  them  shine  in  the  green  glare.  Quartz  is  trans- 
parent to  ultra-violet  light.  When  investigating  ultra-violet 
light,  quartz  lenses  and  prisms  must,  therefore,  be  used. 

Still  higher  frequencies  of  ultra-violet  light  than  those  given 
by  a  condenser  discharge  between  iron  terminals  are  produced  by 
a  low  temperature  mercury  arc.  Obviously  this  arc  must  not  be 


14  RADIATION,  LIGHT,  AND  ILLUMINATION. 

operated  in  a  glass  tube  but  in  a  quartz  tube,  as  glass  is  opaque 
for  these  rays. 

These  ultra-violet  radiations  carry  us  up  to  frequencies  of  about 
3000  X  1012  cycles  per  sec.,  or  to  wave  lengths  of  about  10  X  10~6 
cm.  Then,  however,  follows  a  wide  gap,  between  the  highest 
frequencies  of  ultra-violet  radiation  and  the  frequencies  of  X-rays. 
In  this  gap,  radiations  of  very  interesting  properties  may  some- 
times be  found. 

At  the  extreme  end  of  the  scale  we  find  the  X-rays  and  the 
radiations  of  radio-active  substances  —  if  indeed  these  radiations 
are  wave  motions,  which  has  been  questioned.  Since  at  these 
extremely  high  frequencies  reflection  and  refraction  cease,  but 
irregular  dispersion  occurs,  the  usual  methods  of  measuring  wave 
lengths  and  frequencies  fail.  The  X-rays  apparently  cover  quite 
a  range  of  frequency  and  their  average  wave  length  has  been 
estimated  as  0.01  X  10~6  cm.,  giving  a  frequency  of  3  X  1018 
cycles  per  sec. 

In  comparing  vibrations  of  greatly  differing  frequencies,  the 
most  convenient  measure  is  the  octave,  that  is,  the  frequency  scale 
of  acoustics.  One  octave  represents  a  doubling  of  the  frequency ; 
n  octaves  higher  then  means  a  frequency  2n  times  as  high,  n 
octaves  lower,  a  frequency  Jn  as  high.  By  this  scale  all  the  inter- 
vals are  of  the  same  character;  one  octave  means  the  same 
relative  increase,  which  ever  may  be  the  absolute  frequency  or 
wave  length. 

As  the  perceptions  of  our  senses  vary  in  proportion  to  the  per- 
centual  change  of  the  physical  quantity  causing  the  perception 
(Fechner's  law),  in  the  acoustic  or  logarithmic  scale  the  steps  are 
thus  proportional  to  the  change  of  sensual  perception  caused  by 
them. 

The  visible  radiation  covers  somewhat  less  than  one  octave; 
ultra-violet  radiations  have  been  observed  beyond  this  for  about 
two  more  octaves.  Ten  octaves  higher  is  the  estimated  frequency 
of  X-rays. 

On  the  other  side  of  the  visible  range,  towards  lower  frequencies 
or  longer  waves,  ultra-red  rays,  observations  have  been  extended 
over  more  than  eight  octaves  up  to  wave  lengths  as  great  as  0.03 
cm.  length,  or  frequencies  of  only  10 12  cycles  per  sec.  The  ultra- 
red  rays  given  by  the  heated  silicon  rods  of  our  experiment  do  not 
extend  to  such  low  frequencies,  but  such  very  low  frequencies 


NATURE  AND  DIFFERENT  FORMS  OF  RADIATION.    15 


have  been  observed  in  the  radiations  of  bodies  of  very  low  tem- 
perature, as  liquid  air,  or  in  the  moon's  rays. 

7.   Very  much  longer  waves,  however,  are  the  electric  waves. 
They  are  used  in  wireless  telegraphy,  etc.    I  here  connect  (Fig.  12) 


FIG.  12. 

the  condenser  C  of  the  apparatus  which  I  used  for  operating  the 
ultra-violet  arc,  to  a  spark  gap  Gv  of  which  the  one  side  is  con- 
nected to  ground  Bv  the  other  side  to  a  vertical  aluminum  rod  Alf 
about  8  feet  long.  The  charge  and  discharge  of  the  aluminum 
rod  Al  by  the  oscillating  condenser  current,  send  out  an  electric 
wave  of  about  50  feet  length.  This  wave  passes  through  you,  and 
when  striking  the  aluminum  rod  A2  back  of  you,  induces  therein 
an  electric  charge.  A2  is  separated  from  ground  B2  by  a  narrow 
spark  gap  G2  between  graphite  terminals,  and  the  arrival  of  the 
electric  wave  at  A2  causes  a  small  spark  to  jump  across  the  gap 
Gv  which  closes  the  circuit  of  the  tungsten  lamp  L,  thereby 
lighting  it  as  long  as  the  wave  train  continues. 


16  RADIATION,  LIGHT,  AND  ILLUMINATION. 

The  electric  waves  used  in  wireless  telegraphy  range  in  wave 
lengths  from  100  feet  or  less  to  10,000  feet  or  more,  corresponding 
to  107  to  105  cycles  per  sec. 

Still  very  much  longer  waves  are  the  fields  of  alternating  cur- 
rent circuits:  the  magnetic  and  electrostatic  field  of  an  alterna- 
ting current  progresses  as  a  wave  of  radiation  from  the  conductor. 
But  as  the  wave  length  is  very  great,  due  to  the  low  frequency,  — 

3  X  1010 
a  60-cycle  alternating  current  gives  a  wave  length  of  ^ = 

500  X  10"  cm.  or  3100  miles  —  the  distance  to  which  the  field  of 
the  circuit  extends  is  an  insignificant  fraction  only  of  the  wave 
length,  and  the  wave  propagation  of  the  field  thus  is  usually  not 
considered. 

Electric  waves  of  higher  frequencies  than  used  in  wireless 
telegraphy  are  the  Herzian  waves,  produced  by  electric  oscilla- 
tors, that  is,  a  moderately  long  straight  conductor  cut  in  the 
middle  by  a  gap  and  terminated  by  spherical  condensers,  as 
shown  in  Fig.  13.  On  these  waves  the  velocity  of  propagation 


< EN  ERGY-SU  PPLY- 


o — ^^ — o 


FIG.  13. 

has  been  measured  by  Herz  by  producing  standing  waves  by 
combination  of  main  wave  and  reflected  wave. 

Still  much  higher  frequencies  are  the  oscillations  between  the 
cylinders  of  multi-gap  lightning  arresters,  and  the  limit  of  fre- 
quency of  electric  waves  would  probably  be  given  by  the  oscilla- 
ting discharge  of  two  small  spheres  against  each  other  when 
separated  by  a  narrow  gap.  It  probably  is  at  about  5  X  1010 
cycles,  or  0.6  cm.  wave  length. 

The  blank  space  between  the  longest  electric  wave  and  the 
shortest  ultra-violet  light  wave  thus  has  become  fairly  narrow: 
from  0.6  to  0.03  cm.,  or  only  about  four  octaves. 

8.  In  the  following  tables,  the  different  known  forms  of  radia- 
tion are  arranged  by  their  frequency  and  wave  length,  and  also 
given  in  octaves,  choosing  as  zero1  point  the  middle  c  of  the  piano, 
or  a  frequency  of  128  cycles  per  sec. 


UNIVERSITY 

OF 


NAT 


IFFERENT  FORMS  OF  RADIATION.    17 


SPECTRUM   OF    RADIATION. 

Zero  point  chosen  at  c  =  128  cycles  per  second. 
Speed  of  radiation  S    =  3  X  lu10  cm. 


Cycles. 

Wave  Length  in  Air 
(or  Vacuum). 

Octave:      Q^/ 

£. 

Alternating      current 

1> 

field: 

15 

20,000  km.  =  12,500  mi. 

25 

12.000  km.  =   7,  500  mi. 

3.15 

60 

5,  000  km.  =  3,  100  mi. 

133 

2,250  km.  =   1,400  mi. 

High   frequency   cur-  \ 

rents,    surges    and 

oscillations,    arcing  V 

(9.57) 

31.64 

grounds,     lightning 

phenomena,  etc.        J 

Wireless        telegraph  ( 

105 

3  km.  =  10,000  ft. 

9.63  )    A  ~, 

waves  :                       ( 

107 

30  m.    =      100  ft. 

16.25  \    6'62 

Herzian  waves: 

107 
109 

30  m.    =      100  ft. 
30  cm.  =          1  ft. 

16.25  ) 
22.90  I  12.3 

Limit  of  electric  waves  : 

6X1010 

0.6  cm.  =     0.25  in. 

28.55  )           ) 

First  gap  : 

[4.25] 

Ultra-red  rays  : 

10'2 

4X10' 

30,000x10-"  =0.03  cm. 
76xlO~8  cm. 

3280   )    ftAQ 
41.48  f    b>ba 

Visible  light  rays  :        j 

7.7X10' 

76xlO-6cm. 
39xlO~e  cm. 

41.48  i    ft  Q7 
42.45   ]    U<y/ 

11.6 

Ultra-violet  rays  : 

7.7X10' 
30X101 

39X10-6  cm. 
10  x  10"8  cm. 

42.45   )    ,  Q. 
44.40  f    1'wo 

Second  gap: 

[8.0] 

X-rays  (estimated)  : 

3X10'8 

0.01  xlO~J  cm. 

54.4 

Sound  Waves  : 

Total  : 

57.7  octaves 

Lowest  audible  sound  : 

15 

66  ft.  in  air 

-3.1 

Highest  audible  sound  : 

8000 

1.5  in.  in  air 

+  6.0 

Total  : 

9.1  octaves 

These  radiations  are  plotted  graphically  in  Fig.  14,  with  the 
octave  as  abscissae. 

As  seen,  the  total  range  of  frequencies  of  radiation  is  enormous, 
covering  nearly  60  octaves,  while  the  range  of  sound  waves  is 
only  about  nine  octaves,  from  15  to  8000  cycles. 

There  are  two  blank  spaces  in  the  range  of  radiation,  one  be- 
tween electric  and  light  waves,  and  a  second  and  longer  one 
between  light  and  X-rays. 

It  is  interesting  to  note  that  the  range  of  electric  waves  is  far 
greater  than  that  of  light  waves. 

Only  a  very  narrow  range  of  radiation,  less  than  one  octave  out 
of  a  total  of  60,  is  visible.  It  is  shown  shaded  in  Fig.  14.  This 


18 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


exhibits  the  great  difficulty  of  the  problem  of  efficient  light  pro- 
duction :  it  means  producing  as  large  a  part  of  the  total  radiation 
as  possible  within  this  very  narrow  range  of  visibility. 

Regarding  the  range  of  frequencies  covered  by  it,  the  eye  thus  is 
much  less  sensitive  than  the  ear,  which  hears  over  eight  octaves 
as  sound  waves. 

While  the  visible  radiations  are  the  most  important  ones,  as 
light,  the  total  range  of  radiation  is  of  interest  to  the  electrical 
engineer. 

The  ultra-red  rays  are  those  radiations  which  we  try  to  avoid 
as  far  as  possible  when  producing  light,  as  they  consume  power 


FIG.  14. 

and  so  lower  the  efficiency;  the  ultra-violet  rays  are  of  importance 
in  medicine  as  germ  killers.  They  are  more  or  less  destructive 
to  life,  appear  together  with  the  visible  radiation,  and  where  they 
are  of  appreciable  amount,  as  in  the  arc,  protection  against  them 
becomes  desirable.  The  X-rays  have  become  of  importance  in 
medicine,  etc.,  as  they  penetrate  otherwise  opaque  bodies  and  thus 
allow  seeing  things  inside  of  other  bodies. 

The  total  range  of  electric  waves,  between  the  frequencies  of 
alternating  currents  and  the  limits  of  electric  waves,  has  been  of 
importance  to  the  electrical  engineer  as  harmful  and  destructive 
phenomena  in  electric  circuits,  which  are  to  be  guarded  against, 
and  only  in  recent  years,  with  the  development  of  wireless 
telegraphy,  some  such  electric  waves  have  found  a  useful  com- 
mercial application.  The  main  object  of  their  study  —  which  is 
the  study  of  transient  electric  phenomena,  is  still,  however,  to 
guard  against  their  appearance  in  electric  circuits  and  discharge 
them  harmlessly  when  they  appear. 

Considering  the  great  difference  which  already  exists  between 
alternating  currents  of  low  frequency,  25  or  15  cycles,  and  of  high 


NATURE  AND  DIFFERENT  FORMS  OF  RADIATION.  19 

frequency,  133  cycles,  and  realizing  that  the  total  range  of  waves, 
which  may  appear  in  electric  circuits  is  many  times  greater  than 
the  difference  between  high  and  low  frequency  alternating  cur- 
rents, it  can  be  realized  that  the  differences  in  the  character  of 
electric  waves  are  enormous  between  the  low  frequency  surges  of 
near  machine  frequency  and  the  high  frequency  oscillations  of  a 
multi-gap  lightning  arrester,  near  the  upper  limits  of  electric  wave 
frequencies,  and  the  problem  of  protecting  circuits  against  them 
thus  is  vastly  more  difficult  than  appears  at  first  sight  and  the 
conclusions  drawn  from  experimental  investigations  of  electric 
waves  may  be  very  misleading  when  applied  to  waves  many 
octaves  different  from  those  used  in  the  experiment.  This  ex- 
plains the  apparently  contradictory  evidence  of  many  experi- 
mental investigations  on  the  protection  of  electric  circuits. 


LECTURE  II. 
RELATION   OF   BODIES   TO    RADIATION. 

9.  For  convenience,  the  total  range  of  known  radiations  can 
be  divided  into  two  classes,  the  electric  waves  and  the  light  waves, 
which  are  separated  from  each  other  by  the  blank  space  in  the 
middle  of  the  spectrum  of  radiation  (Fig.  14).  Under  light 
waves  we  here  include  also  the  invisible  ultra-red  radiation  and 
the  ultra-violet  radiation  and  the  non-refrangible  radiations,  as 
X-rays,  etc.,  separated  from  the  latter  by  the  second  blank 
space  of  the  radiation  spectrum. 

In  the  following,  mainly  the  light  waves,  that  is,  the  second  or 
high  frequency  range  of  radiation,  will  be  discussed.  The  elec- 
tric waves  are  usually  of  importance  only  in  their  relation  to  the 
radiator  or  oscillator  which  produces  them,  or  to  the  receiver  on 
which  they  impinge,  and  thus  are  treated  in  connection  with  the 
radiator  or  receiver,  that  is,  the  electric  conductor,  in  the  theory 
of  transient  electric  phenomena  and  oscillations.* 

The  radiation  may  be  of  a  single  frequency,  that  is,  a  single 
wave;  or  a  mixture  of  different  frequencies,  that  is,  a  mixture 
of  different  and  frequently  of  an  infinite  number  of  waves. 

Electric  radiation  usually  is  of  a  single  frequency,  that  is,  of  the 
frequency  or  wave  length  determined  by  the  constants  of  the 
electric  circuit  which  produces  the  radiation,  mainly  the  induct- 
ance L  and  the  capacity  C.  They  may,  however,  have  different 
wave  shapes,  that  is,  comprise,  in  adolition  to  the  fundamental 
wave,  higher  harmonics  or  multiples  thereof,  just  as  the  sound 
waves  which  represent  the  same  tone  with  different  musical 
instruments  are  of  the  same  frequency  but  of  different  wave 
shapes,  that  is,  contain  different  higher  harmonics. 

Light  radiations  usually  are  a  mixture  of  a  number  of  waves  of 
different  frequencies,  and  very  commonly  a  mixture  of  an  infinite 
number  of  frequencies,  as  is,  for  instance,  the  case  with  the 

*  "Theory  and  Calculation  of  Transient  Electric  Phenomena  and  Oscilla- 
tions. " 


RELATION  OF  BODIES  TO  RADIATION.  21 

radiation  of  an  incandescent  body  as  a  lamp  filament,  which 
contains  all  the  frequencies  from  long  ultra-red  waves  over 
visible  light  waves  to  ultra-violet  waves. 

In  the  action  of  vibrations  on  our  senses  there  is  a  characteristic 
difference  between  the  perception  of  sound  waves  by  the  ear  and 
that  of  light  waves  by  the  eye :  the  ear  is  analytic,  that  is,  can 
separate  the  individual  waves  in  a  mixture  of  different  sound 
waves,  as  an  accord  on  the  piano,  and  distinguish  the  individual 
components  of  the  mixed  sound  which  reaches  the  ear.  Thus 
we  can  hear  and  distinguish  an  individual  voice  amongst  a  mass 
of  other  noises.  The  eye,  however,  perceives  only  the  resultant 
of  all  -the  visible  radiations  which  reach  it,  but  cannot  separate 
their  components,  and  very  different  mixtures  of  radiations  thus 
make  the  same  impression  upon  the  eye:  thus,  for  instance, 
numerous  mixtures  of  blue  and  yellow  light  appear  alike  to  the 
eye  and  the  same  as  green  light,  that  is,  appear  green,  while 
physically,  it  is  obvious  that  mixtures  of  blue  and  yellow  light 
are  essentially  different  from  green  light. 

It  is  interesting  to  imagine  how  nature  would  look  to  us  if  the 
eye  were  analytic,  that  is,  could  separate  the  different  component 
radiations,  and  if  it  could  perceive  waves  over  as  great  a  range  of 
frequency  as  the  ear,  about  nine  octaves  instead  of  less  than  one 
octave  as  is  now  the  case.  The  information  given  to  us  by  the 
sense  of  sight  would  be  infinitely  increased,  and  we  would  see 
many  differences  and  changes  which  now  escape  us. 

10.  However,  while  the  eye  cannot  distinguish  the  different 
component  radiations  but  sees  only  their  resultant,  the  specific 
effects  of  the  component  radiations,  as  the  physiologically  harm- 
ful action  of  an  ultra-violet  component  of  light,  still  remain,  even 
if  the  eye  does  not  see  the  components,  and  in  the  study  of  radia- 
tion for  the  purpose  of  its  engineering  use  for  illumination  it  is 
therefore  necessary  to  analyze  the  mixed  radiation  given  by  a 
source  as  a  lamp,  by  resolving  it  into  its  component  waves. 

This  is  done  by  using  some  feature  of  the  radiation  which 
varies  with  the  frequency.  Such  is  the  case  with  the  velocity  of 
propagation. 

The  velocity  of  light  in  empty  space  is  3  X  1010  cm.  per  sec. 
It  is  practically  the  same  in  air  and  other  gases.  In  denser 
bodies,  however,  as  water,  glass,  etc.,  the  velocity  of  light  is  less 
and,  as  will  be  seen,  is  different  for  different  frequencies. 


22 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


Assume  then,  in  Fig.  15,  a  beam  of  light  B  striking  under  an 
angle  the  boundary  between  two  media,  as  air  A  and  water  W, 
the  vibration  of  the  ether  particles  in  the  beam  of  light  is  at  right 
angles  to  the  direction  of  propagation  BC,  and  successively  the 
waves  thus  reach  at  blf  a2  bz  .  .  .  As  soon,  however,  as  the  back 
edge  of  the  beam  reaches  the  boundary  at  D  its  speed  changes 


FIG.  15. 

by  entering  the  medium  W  —  decreases  in  the  present  instance. 
Let  then  Sl  =  speed  of  propagation  in  medium  A,  S2  =  speed  of 
propagation  in  medium  W.  Then,  while  the  center  of  the  beam 
moves  the  distance  EC,  the  back  edge,  in  the  denser  medium, 

a 

moves  only  the  distance  DI  =  -^EC,  and  the  wave  front  of  the 

»i 
back  half  of  the  beam  thus  changes  to  CI  while  that  of  the  front 

half  of  the  beam,  which  is  still  in  the  medium  A,  remains  GC. 
Then,  while  the  front  edge  of  the  beam  moves  from  G  to  H,  the 
center  and  the  whole  back  half  of  the  beam  moves  in  the  denser 

o 

medium  TF,  only  the  distance  CK  =  — 2  GH,  and  the  wave  front 

«i 

of  the  beam,  in  the  medium  TF,  now  is  EL.  That  is,  due  to  the 
difference  in  velocity  in  the  two  media  A  and  W,  the  wave  front 
of  the  beam,  and  thereby  its  direction  of  propagation,  is  changed 


RELATION  OF  BODIES  TO  RADIATION.  23 

when  traversing  the  boundary  between  the  two  media,  and  the 
beam  EC  continues  its  motion  in  the  direction  CM. 

Let  then  o^  =  angle  of  incidence,  that  is,  the  angle  between 
the  incident  beam  BC  and  the  perpendicular  CN  on  the  boundary, 
and  a2  =  angle  of  refraction,  that  is,  the  angle  between  the  out- 
going or  refracted  beam  CM  and  the  perpendicular  CP  on  the 
boundary.  It  is  then : 

FDH  =  a,  and  LHD  =  a2  ; 
hence, 

FH  =  DH  sin  a,  and  DL  =  DH  sin  av       (1) 

The  front  edge  of  the  beam  moves  the  distance  FH  in  medium 
A,  while  the  back  edge  moves  the  distance  DL  in  medium  W; 
that  is, 

FH  +  DL  =  S,  -  S3;  (2) 


hence,  substituting  (1)  into  (2),  gives: 

sin  «1      Sl 


sn 


(3) 


That  is,  the  ratio  of  the  sines  of  the  angle  of  incidence  and  the 
angle  of  refraction  equals  the  ratio  of  the  speed  of  propagation 
in  the  two  media,  hence  the  ratio  of  the  sines  of  these  two  angles 
is  constant.  This  is  the  law  of  refraction,  and  this  ratio  of  sines 
is  called  the  refractive  index  between  the  two  media  A  and  W.  As 
the  refractive  index  of  one  medium  W,  then,  is  understood  its  re- 
fractive index  against  empty  space  or  against  air  : 


sn  a 


where  S  is  the  velocity  of  light  in  empty  space  =  3  X  1010,  and 
Sl  the  velocity  in  the  medium,  of  which  ^  is  called  the  refractive 
index. 

From  equation  (4)  it  follows,  that,  if  ^_2  is  the  refractive  index 
between  medium  1  and  medium  2,  £2_3,  the  refractive  index 
between  medium  2  and  medium  3,  dl-3  =  £2_3  -*-  ^_2  =  refractive 
index  of  medium  1  and  medium  3;  that  is,  the  refractive  index 
between  any  two  media  is  derived  as  the  ratio  of  their  refractive 
indices  against  a  third  medium,  as,  for  instance,  against  air. 


24  RADIATION,  LIGHT,  AND  ILLUMINATION. 

11.  Incidentally,  it  is  interesting  to  consider  the  corresponding 
relations  in  electric  waves. 

In  an  electric  circuit,  the  speed  of  propagation  of  an  electric 
wave  is,  when  neglecting  the  energy  losses  in  and  by  the  con- 
ductor: 

S  =  -L=  ,  (5) 

VLC 

where  L  is  the  inductance,  C  the  capacity  of  the  conductor  per 
unit  length  (the  length  measured  in  the  same  measure  as  the 
speed  S). 

The  inductance  L  is  proportional  to  the  permeability  /*,  and 
the  capacity  C  proportional  to  the  dielectric  constant,  or  specific 
capacity  K  of  the  medium  surrounding  the  conductor,  that  is,  the 
medium  through  which  the  electric  wave  propagates;  that  is, 


A  V  p* 

where  A  is  a  proportionality  constant. 

The  ratio  of  the  speed  of  propagation  of  an  electric  wave  in  two 
media  1  and  2  thus  is: 

<,, 


for  empty  space,  fj.  =  1  and  «  =  1; 
hence, 


(8) 


where  Sl  is  the  speed  of  propagation  in  the  medium  of  constants 
/^  and  jcr 
Comparing  equation  (8)  with  (4)  it  follows  : 

Vl  =  d*-,  (9) 

that  is,  the  square  of  the  refractive  index  d  equals  the  product  of 
permeability  JJL  and  dielectric  constant  K. 

Since  for  most  media  the  permeability  /JL  =  1,  for  all  except 

e  maneti    mri 


the  magnetic  materials 


RELATION  OF  BODIES  TO  RADIATION. 


25 


This  relation  between  the  constant  of  the  electric  circuit  K  and 
the  constant  of  optics  d  was  one  of  the  first  evidences  of  the 
identity  of  the  meclium  in  which  the  electric  field  exists  with 
the  medium  which  carries  the  light  waves.  It  is,  however,  only 
approximately  correct,  as  the  refractive  index  d  varies  with  the 
frequency  and  is  derived  for  the  extremely  high  frequencies  of 
light  radiation,  while  K  refers  to  stationary  conditions.  A  better 
agreement  is  thus  reached  when  using  as  d  the  refractive  index 
extrapolated  for  infinite  wave  lengths. 

12.  It  is  found  that  the  different  component  frequencies  of  a 
beam  of  radiation  are  deflected  differently  when  passing  from  one 
medium  into  another,  and  the  higher  frequencies  are  deflected 


FIG.  16. 

more  than  the  lower  frequencies,  thus  showing  that  the  velocity 
of  propagation  decreases  with  an  increase  of  frequency,  that  is, 
a  decrease  of  wave  length. 

This  gives  a  means  of  resolving  a  mixed  radiation  into  its  com- 
ponent waves,  that  is,  into  a  spectrum,  by  refraction. 

A  narrow  beam  of  light  B  (Fig.  16)  is  passed  through  a  prism  P 
of  transparent  material,  and  the  component  frequencies  then 
appear  on  the  screen  A  (or  are  seen  by  the  eye)  side  by  side,  the 
red  R  to  the  left,  the  violet  V  to  the  right,  in  Fig.  16,  and  the  green 
G  in  the  middle. 

It  is  obvious  that  the  material  of  the  prism  must  be  transparent 
to  the  radiation;  thus,  when  studying  ultra-violet  radiation  to 
which  glass  is  opaque,  glass  prisms  cannot  be  used,  but  some 
material  transparent  to  ultra-violet  light  such  as  a  quartz  prism 
must  be  used. 


26 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


The  beam  of  light  also  can  be  resolved  into  its  components  by 
a  diffraction  grating,  in  which  case  the  lower  frequencies  are 
deflected  more  than  the  higher  frequencies ;  that  is,  the  red  more 
than  the  violet. 

These  two  forms,  the  refracting  spectroscope  and  the  diffract- 
ing spectroscope,  now  enable  us  to  resolve  a  beam  of  mixed  radia- 
tion into  its  components  and  thus  study  its  spectrum. 

13.   I  show  you  here  a  number  of  typical  spectra: 

(1).  The  spectra  of  an  incandescent  lamp  and  an  alcohol 
lamp  with  Welsbach  mantel.  These  are  continuous  spectra,  that 
is,  show  all  the  radiations  from  red  over  orange,  yellow,  green, 
blue,  indigo  to  violet,  uniformly  shading  into  each  other. 

(2a).  The  spectrum  of  the  mercury  lamp.  This  is  a  line 
spectrum,  that  is,  shows  only  a  finite  number  of  bright  lines  on 
black  background.  It  contains  five  bright  lines ;  greenish  yellow, 
bright  green,  indigo  and  two  violet,  one  faint  dark  green  line,  and 


1                1  1 

1             1  1 

1           Ij 

RED 

ORANGE   1  YELLOW  1                GREEN 

BLUE 

INDIGO 

VIOLET 

FIG.  17. 

a  number  of  very  faint  red  and  orange  lines,  of  which  three  are 
indicated  dotted  in  Fig.  17. 

(26).  The  spectrum  of  an  arc  between  titanium  carbide  elec- 
trodes. This  also  is  a  line  spectrum,  but  unlike  the  mercury 
spectrum,  which  has  only  six  bright  lines,  the  titanium  spectrum 
contains  many  thousands  of  bright  lines,  so  that  with  the  low 
power  of  the  spectroscope  which  you  have,  the  lines  blurr  into 
each  other  and  we  see  only  the  most  prominent  or  brightest  lines 
on  a  uniformly  luminous  background,  which  latter  requires  a 
more  powerful  spectroscope  to  resolve  into  lines. 

(3) .  The  band  spectrum.  This  shows  a  number  of  bright  bands, 
frequently  gradually  fading  out  at  their  edge  and  separated  by 
dark  spaces.  It  thus  differs  from  the  continuous  spectrum  (1)  in 
being  discontinuous,  that  is,  missing  certain  ranges  of  frequency, 
and  differs  from  the  line  spectrum  (2)  in  that  the  band  spectrum 
has  a  number  or  range  of  frequencies  in  each  band,  where  the  line 


RELATION  OF  BODIES  TO  RADIATION.  27 

spectrum  has  only  'one  single  frequency  in  each  line.  Such 
band  spectra  are  usually  characteristic  of  luminescent  compounds 
or  of  gases  and  vapors  at  high  pressure,  while  elementary  gases 
or  vapors  give  line  spectra.  Absorption  and  fluorescence  also 
give  band  spectra,  and  I  thus  show  you  a  band  spectrum  by  opera- 
ting a  mercury  lamp  in  a  tube  of  uranium  glass,  behind  a  trans- 
parent screen  colored  by  rhodamine  (an  aniline  dye  which 
fluoresces  red).  As  you  see,  the  spectrum  shows  a  broad  red 
band,  due  to  the  reddish  screen,  and  a  greenish  yellow  band  due 
to  the  uranium  glass,  while  the  normal  mercury  lines  are  de- 
creased in  intensity. 

(4).  If  you  now  look  with  the  spectroscope  at  the  Welsbach 
mantel  through  the  mercury  arc  stream,  you  see  the  continuous 
spectrum  of  the  mantel  and  superimposed  upon  it  the  line  spec- 
trum of  the  mercury  lamp.  The  light  giving  mercury  vapor  thus 
is  transparent  for  the  light  of  the  Welsbach  mantel  back  of  it,  and 
lets  it  pass  through,  with  the  exception  of  those  particular  fre- 
quencies which  it  gives  itself;  that  is,  a  luminous  gas  absorbs 
those  frequencies  of  radiation  which  it  produces,  but  is  trans- 
parent for  all  other  frequencies.  This  is  easily  understood:  an 
atom  on  which  a  vibration  impinges  will  be  set  in  motion  by  it 
and  thus  absorb  the  energy  of  the  impinging  vibration  if  it  is  able 
to  vibrate  with  the  frequency  of  the  impinging  vibration;  that  is, 
to  resonate  with  it,  but  will  not  be  affected  by  any  other  frequency 
to  which  it  cannot  respond,  and  thus  is  transparent  to  all  frequen- 
cies of  vibration,  except  to  those  to  which  it  can  respond;  that  is, 
which  it  produces  when  vibrating. 

When  looking  at  a  continuous  spectrum  through  a  luminous 
gas  or  vapor,  two  cases  thus  may  occur:  either  the  spectrum  lines 
of  the  gas  are  brighter  than  the  continuous  spectrum,  as  in  the 
present  case,  and  then  appear  as  bright  lines  on  a  bright  back- 
ground, or  the  continuous  spectrum  is  brighter  than  the  lines  of 
the  gas  spectrum  in  front  of  it  and  the  lines  of  the  gas  spectrum 
appear  less  bright  than  the  background,  that  is,  appear  as  dark 
lines  on  a  bright  background.  Such  a  spectrum  is  called  a 
reversed  spectrum,  or  absorption  spectrum.  It  shows  the  lines  of 
the  gas  or  vapor  spectrum,  by  contrast,  dark  on  the  brighter  back- 
ground of  the  continuous  spectrum. 

The  sun  and  many  fixed  stars  present  such  a  reversed  spectrum : 
the  sun's  spectrum  shows  the  spectrum  lines  of  all  the  elements 


28 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


which  are  in  the  sun's  atmosphere  as  dark  lines  on  the  continuous 
spectrum  given  by  the  inner  core  of  the  sun. 

Whether  the  line  spectrum  of  a  gas  or  vapor  is  reversed  by  the 
continuous  spectrum  of  a  solid  or  liquid  back  of  it  or  not  depends 
upon  the  relative  intensity,  and  thus,  to  some  extent,  on  the  rela- 
tive temperature.  Some  fixed  stars  show  bright  lines  on  a  less 
luminous  background,  due  possibly  to  a  higher  temperature  and 
greater  thickness  of  their  atmosphere,  and  sometimes  bright  lines 
and  dark  lines  occur  simultaneously,  or  dark  lines  may  change  to 
bright  lines  at  such  places  at  which,  by  some  activity,  as  a  tem- 
perature rise,  their  brilliancy  is  greatly  increased. 


FIG.  18. 

Combinations  of  the  different  types  of  spectra:  continuous 
spectrum,  line  spectrum,  band  spectrum,  reversed  spectrum, 
frequently  occur,  as  we  have  seen  bands  and  lines  together  in  the 
modified  mercury  spectrum,  and  in  this  case,  by  turning  on  an 
incandescent  lamp,  we  can  still  add  a  continuous  spectrum  due 
to  the  light  of  the  incandescent  lamp  reflected  from  the  walls  of 
the  room.  So  also  in  the  continuous  spectrum  of  incandescent 
bodies,  bright  bands  or  dark  bands  occasionally  appear,  that  is, 
regions  in  the  spectrum  of  greater  or  lesser  intensity,  as  will  be 
discussed  in  the  paragraphs  on  colored  radiation  and  selective 
radiation. 


RELATION  OF  BODIES  TO  RADIATION. 


29 


14.  When  a  beam  of  radiation  impinges  upon  a  body  it  is 
resolved  into  three  parts :  one  part  is  reflected,  that  is,  does  not 
enter  the  body  at  all,  but  is  thrown  back.  The  second  part  is 
absorbed  in  the  body,  that  is,  converted  into  another  form  of 
energy  (which  other  form  of  energy  usually  is  heat,  but  may  be 
chemical  energy,  some  other  frequency  of  radiation,  etc.)  and  the 
third  part  is  transmitted,  that  is,  passes  through  the  body,  and 
out  of  it,  if  the  body  is  not  too  thick.  No  body  reflects,  or 
absorbs,  or  transmits  all  the  radiations,  but  even  the  most  per- 
fectly reflecting  body  absorbs  and  transmits  some  radiation,  the 
most  transparent  body  reflects  and  absorbs  some  radiation,  etc. 

Reflection  may  be  either  regular  reflection,  or  irregular  reflec- 
tion. In  the  former  case  (Fig.  18)  the  beam  of  light  is  reflected 
under  the  same  angle  under  which  it  impinges  upon  the  body, 
and  the  body  thus  acts  as  a  mirror,  that  is,  gives  a  virtual  image 


FIG.  19. 

back  of  it  as  shown  in  dotted  line  in  Fig.  18.  In  the  latter  case 
(Fig.  19)  the  light  is  reflected  irregularly  in  all  directions. 

A  body  which  reflects  all  the  frequencies  of  radiation  uniformly, 
that  is,  in  which  the  percentage  of  the  impinging  radiation,  which 
is  reflected,  is  the  same  for  all  frequencies  of  radiation,  is  called  a 
colorless  body,  and  a  body  which  reflects  a  higher  percentage  of  the 
radiation  of  some  frequency  than  of  other  frequencies,  is  called 
a  colored  body,  and  its  color  is  the  color  of  radiation,  that  is, 
the  frequency  or  frequencies  which  it  reflects  more  than  other 
frequencies. 

A  colorless  body  which  reflects  all  the  radiation  impinging  upon 
it  is  called  a  white  body.  Most  nearly  white  bodies  are  silver, 
magnesia,  chalk,  etc.  A  body  which  reflects  none  of  the  radiation 
impinging  upon  it,  but  absorbs  all,  is  called  a  block  body.  The 


30  RADIATION,  LIGHT,  AND  ILLUMINATION. 

most  nearly  black  bodies  are  lampblack,  charcoal,  etc.  A  body 
which  reflects  a  constant  part  of  the  impinging  radiation,  that  is, 
the  same  part  or  percentage  for  all  frequencies,  is  called  a  grey 
body,  and  the  ratio  of  the  reflected  light  to  the  total  impinging 
light  is  called  its  whiteness  or  albedo.  A  perfectly  white  body 
thus  has  albedo  1,  a  perfectly  black  body  albedo  0,  and  a  body 
which  reflects  one-quarter  and  absorbs  the  other  three-quarters 
of  the  radiation  of  any  wave  length  impinging  upon  it,  would  be 
said  to  have  albedo  0.25. 

Black,  white  and  grey  thus  are  not  considered  as  colors  in 
physics. 

As  examples  of  colorless  bodies  I  show  you  here : 

Regular  reflection:  polished  silver,  white;  polished  iron,  grey. 

Irregular  reflection:  powdered  magnesia,  white;  lampblack, 
black;  powdered  zinc,  barium  sulphide,  grey. 

As  example  of  colored  bodies  I  show  you : 

Regular  reflection:  polished  copper,  red;  polished  gold  or 
brass,  yellow. 

Irregular  reflection:  mercury  sulphide  (cinnabar),  red;  potas- 
sium bichromate,  orange;  magnesium  chromate,  yellow;  copper 
acetate-arsenite  (paris  green),  green;  copper  oxide  hydrate 
precipitated  by  ammonia,  blue;  ultra-marine,  indigo ;  magnesium 
permanganate  mixed  with  magnesia,  violet. 

15.  Of  the  radiation  which  enters  a  body,  that  part  which  is 
absorbed  is  usually  converted  into  heat.  Thus  a  black  body, 
when  exposed  to  radiation,  becomes  hotter  than  a  white  body, 
which  reflects,  or  a  transparent  body,  which  transmits,  most 
of  the  radiation.  Thus  the  globe  of  a  colored  incandescent  lamp, 
which  absorbs  more  of  the  radiation  than  a  transparent  globe, 
becomes  hotter  than  a  clear  glass  globe.  When  scattering  dirt 
on  the  snow  it  can  be  made  to  melt  down  far  more  rapidly  in  the 
spring,  under  the  rays  of  the  sun,  than  when  remaining  clean,  etc. 

Some  bodies  convert  the  absorbed  radiation  into  chemical 
energy,  into  other  frequencies  of  radiation,  etc. 

Bodies  which  convert  the  absorbed  radiation,  or  rather  a  part 
thereof,  into  radiation  of  different,  as  far  as  known  always 
lower,  frequencies,  are  called  fluorescent  bodies.  Thus  the  solu- 
tion of  rhodamine  in  alcohol,  which  I  show  you  here,  fluoresces 
red.  It  transmits  red  light,  but  absorbs  green,  blue  and  violet 
light,  and  converts  a  part  thereof  into  red  light.  This  is  best 


RELATION  OF  BODIES  TO  RADIATION.  31 

illustrated  by  exhibiting  it  in  a  source  of  light  which  contains  no 
red  rays,  as  the  mercury  lamp.  You  see  in  the  rays  of  the  mer- 
cury lamp  the  rhodamine  solution  looks  bright  red,  the  red  light 
seems  to  come  from  the  inside  of  it,  and  especially  through  a  red 
glass  the  solution  looks  like  a  red  hot  incandescent  body.  Here 
then,  as  no  red  light  reaches  the  solution,  the  red  light  given  by  it 
must  be  produced  by  frequency  conversion  from  other  radiation. 
The  spectroscope  shows  especially  the  bright  green  mercury  line 
weakened. 

The  phenomena  of  conversion  of  absorbed  light  into  other 
forms  of  energy  will  be  more  fully  discussed  in  the  following 
paragraphs. 

16.  By  the  transmitted  light,  that  is,  the  radiation  which 
passes  through  them,  bodies  are  again  divided  into  colorless 
bodies;  that  is,  such  bodies  which  transmit  the  same  percentage 
of  radiation  for  every  wave  length  or  frequency,  and  colored 
bodies;  that  is,  bodies  which  transmit  a  larger  percentage  of 
radiation  of  some  frequencies  than  of  others,  and  as  the  trans- 
parent color  of  a  body,  then,  is  understood  the  color,  that  is,  the 
frequency,  of  that  radiation  of  which  the  greatest  percentage  is 
transmitted.  Thus  a  red  glass  is  one  which  transmits  a  higher 
percentage  of  red  radiation  than  of  any  other  radiation. 

A  body,  then,  is  called  transparent,  if  it  transmits  all  the  radia- 
tion, and  opaque,  if  it  transmits  no  radiation,  but  absorbs  or 
reflects  all.  If  only  a  part  of  the  radiation  is  transmitted,  but 
in  such  manner  that  it  is  the  same  part  for  all  frequencies,  the 
body  is  called  grey;  or  imperfectly  transparent,  if  the  part  which 
is  not  transmitted  is  absorbed  in  the  body ;  and  translucent,  if 
the  part  which  is  not  transmitted  is  irregularly  reflected  inside 
of  the  body. 

The  most  perfectly  transparent  bodies,  for  visible  light,  are 
glass,  water,  quartz,  etc. ;  the  most  opaque  are  the  metals,  and 
perfectly,  or  almost  perfectly  opaque  are  the  magnetic  metals, 
perhaps  due  to  the  very  low  speed  of  propagation  in  these  metals, 
which  would  result  from  the  high  value  of  the  permeability  /*  by 
equation  (8)  paragraph  11. 

As  example  of  colorless  bodies  I  show  you  here  a  glass  tube 
filled  with  water,  transparent;  a  tube  filled  with  nigrosine  solu- 
tion in  alcohol,  opaque  and  black;  a  very  diluted  solution  of 
nigrosine  with  traces  of  other  aniline  dye  for  color  correction,  in 


32  RADIATION,  LIGHT,  AND  ILLUMINATION. 

alcohol,  as  grey,  and  a  tube  filled  with  an  emulsion  of  water  with 
a  solution  of  chloroform  in  white  paraffin  oil,  which  latter  solu- 
tion has  the  same  specific  gravity  as  water,  translucent. 

Samples  of  transparent  colored  bodies  are:  carmine  solution, 
red;  potassium  bichromate  solution,  orange;  potassium  chromate 
solution,  yellow;  nickel  sulphate  solution,  green;  copper  nitrate 
solution,  blue;  diluted  potassium  permanganate  solution,  or 
diluted  solution  of  iodine  in  chloroform,  violet. 

As  seen,  the  terms  " colorless"  and  " colored"  have  two  dif- 
ferent meanings  when  applied  to  the  reflected  radiation  and 
when  applied  to  the  transmitted  radiation,  and  the  color  of  a 
body  in  reflected  light  may  be  different,  and  frequently  is  differ- 
ent, from  its  color  in  transmitted  light,  and  some  bodies  may  be 
colorless  in  reflected  light,  but  colored  in  transmitted  light,  and 
inversely.  In  materials  of  low  absorption,  the  transmitted  and 
the  reflected  colors  must  be  approximately  complimentary ;  thus 
the  transmitted  color  of  the  atmosphere  is  orange,  the  reflected 
color  blue. 

17.  Colors  are,  therefore,  distinguished  into  opaque  colors  and 
transparent  colors.  The  opaque  colors  are  those  shown  by  the 
light  reflected  from  the  body,  the  transparent  colors  those  shown 
by  the  light  transmitted  through  the  body.  In  reflected  light, 
the  transparent  colors,  therefore,  show  only  when  covering  a 
white,  that  is,  reflecting  surface,  and  then,  due  to  the  light 
reflected  from  the  white  background  of  the  transparent  coloring 
body  traversing  this  body  twice,  before  and  after  reflection,  and, 
therefore,  depend  in  their  brilliancy  on  the  background.  The 
difference  between  opaque  and  transparent  colors,  the  former 
reflecting  from  the  surface,  the  latter  reflecting  from  back  of 
the  colored  substance,  is  seen  by  comparing  the  appearance  of 
the  two  classes  of  colors  shown  in  14  and  in  16. 

In  its  general  use,  the  terms  colorless,  white,  black,  transparent, 
opaque,  refer  only  to  the  visible  radiation,  that  is,  to  the  frequen- 
cies within  that  octave  which  the  eye  perceives  as  light.  More 
broadly,  however,  these  terms  may  in  physics  be  applied  to  the 
total  range  of  radiation,  and  then  many  substances  which  are 
colorless  for  visible  light,  would  be  considered  as  strongly  colored, 
that  is,  show  for  different  frequencies  great  differences  in  the  per- 
centage of  radiation  which  they  reflect  or  transmit.  Thus  we 
have  seen  that  glass,  which  is  transparent  for  visible  light,  is 


RELATION  OF  BODIES  TO  RADIATION.  33 

entirely  opaque  for  some  ultra-violet  light  and  also  opaque  for 
ultra-red  light  of  low  frequency,  so  in  this  broader  sense  would 
have  to  be  called  colored*  the  color  of  clear  glass,  however,  is  that 
of  the  visible  spectrum;  or,  for  instance,  iodine  solution,  which  is 
opaque  for  visible  light,  is  transparent  for  ultra-red  light,  that  is, 
its  color  is  ultra-red,  etc. 

In  this  broader  sense,  referring  to  the  total  range  and  not 
merely  to  the  visible  range,  glass,  water,  mica,  etc.,  are  not  color- 
less transparent  but  colored,  and  quartz  is  probably  the  most 
transparent  and  colorless  body. 

18.  The  color  of  the  body,  thus,  is  represented  by  that  fre- 
quency or  those  frequencies. of  radiation  of  which  a  higher  per- 
centage are  reflected  or  transmitted  than  of  the  other  frequencies 
of  radiation.  This  color,  therefore,  is  a  characteristic  property 
of  the  body  and  independent  of  the  character  of  the  light  and  of 
its  physiological  effect  on  the  eye,  and  can  thus  be  called  the 
actual  or  objective  color  of  the  body.  If  we  consider  diffused 
daylight  as  white,  then  the  body  appears  to  the  eye  in  its 
objective  or  actual  color  when  compared  with  a  white  body, 
that  is,  a  body  uniformly  reflecting  all  radiation  in  the  diffused 
daylight.  Under  other  conditions,  as,  for  instance,  in  artificial 
illumination,  bodies  do  not  always  appear  to  the  eye  in  their 
objective  colors,  but  may  show  a  very  different  color  depending 
on  the  character  of  the  source  of  light.  For  instance,  I  have 
here  a  plate  of  colored  glass :  looking  through  it  at  the  mercury 
lamp  you  see  the  glass  has  an  olive  green  color;  but  when  I  turn 
on  an  incandescent  lamp  you  see  that  it  is  ordinary  red  glass. 
Its  objective  color  is  red,  its  subjective  color  in  the  mercury 
light  is  green.  Looking  through  this  glass  in  daylight  it 
appears  red  as  it  transmits  more  red  light  than  other  colors  of 
light,  and  the  transmitted  light  thus  contains  a  higher  per- 
centage of  red  rays  than  diffused  daylight.  The  rays  of  the 
mercury  lamp,  however,  contain  very  little  red  light  and  very 
much  green  light,  and  while  by  this  red  glass  a  much  higher 
percentage  of  the  red  light  from  the  mercury  lamp  is  trans- 
mitted than  of  its  green  light,  this  higher  percentage  of  trans- 
mitted red  light  is  very  much  less  than  the  lower  percentage  of 
the  transmitted  green  light,  and,  therefore,  in  the  transmitted 
light,  green  still  preponderates  more  than  in  the  diffused  day- 
light, that  is,  the  glass  appears  green.  For  instance,  if  in  the 


34  RADIATION,  LIGHT,  AND  ILLUMINATION. 

mercury  lamp  the  ratio  of  red  light  to  green  light  is  only  one 
hundredth  of  what  it  is  in  daylight,  and  the  red  glass  transmits 
ten  times  as  high  a  percentage  of  red  as  of  green  light,  then  in 
the  light  of  the  mercury  lamp  transmitted  through  this  red  glass 
the  ratio  of  red  light  to  green  light  is  still  only  one-tenth  of  what 
it  is  in  daylight,  and  the  glass  thus  appears  green. 

We  have  to  distinguish  between  the  actual  or  objective  color  of  a 
body,  which  is  a  constant  of  the  body,  and  its  apparent  or  sub- 
jective color,  which  depends  upon  the  light  in  which  we  view  the 
body,  and  therefore  may  be  very  different  for  different  illumi- 
nants,  and  bodies  which  have  the  same  colors  in  one  illuminant 
may  have  entirely  different  colors  in  another  illuminant  and 
inversely.  It  is,  however,  the  subjective  color  of  the  body  cor- 
responding to  the  particular  illuminant  used  which  we  see,  and 
which  is,  therefore,  of  importance  in  illuminating  engineering, 
and  the  study  of  the  subjective  colors,  therefore,  is  of  foremost 
importance,  and  the  success  or  failure  of  an  illumination  depends 
on  the  production  of  the  desired  subjective  colors. 

19.  Broadly,  an  illumination  discriminates  for  the  color  in 
which  it  is  deficient  and  the  color  in  which  it  is  rich.  The  color 
in  which  the  illuminant  is  deficient  —  as  red  in  the  mercury  lamp, 
blue  and  violet  in  the  incandescent  lamp  —  appears  black;  the 
color  in  which  the  illuminant  is  abnormally  rich  —  as  yellow  in 
the  incandescent  lamp,  green  in  the  mercury  lamp  —  appears  as 
white ;  that  is,  both  colors  disappear,  more  or  less ;  as  colors,  be- 
come colorless.  Thus  in  the  yellow  incandescent  lamp,  opaque 
yellow  appears  the  same  as  white,  opaque  blue  and  violet  appear 
more  or  less  as  black;  transparent  yellow  appears  colorless,  trans- 
parent blue  and  violet  appear  colorless  and  from  light  transparent 
grey  to  opaque  black.  In  the  green  mercury  lamp,  opaque  green 
and  white  appear  the  same,  opaque  red  appears  as  black;  trans- 
parent green  appears  colorless,  and  transparent  red  appears 
colorless,  from  clear  transparent  to  grey,  to  opaque  black,  de- 
pending upon  its  intensity. 

It  is  interesting  to  see  the  difference  between  opaque  and 
transparent  colors  in  this  respect:  as  opaque  colors  the  deficient 
color  turns  black,  the  excess  color  white;  but  as  transparent 
colors  both  become  colorless  and  more  or  less  transparent.  Thus, 
in  the  mercury  lamp,  red  and  green  as  transparent  colors  both 
vanish,  or  rather,  very  greatly  decrease  in  their  prominence. 


RELATION  OF  BODIES  TO  RADIATION.  35 

As  the  eye  perceives  only  the  resultant  of  radiation,  very  dif- 
ferent combinations  of  radiation  may  give  the  same  impression 
to  the  eye,  but  when  blotting  out  certain  radiations,  as  red  and 
green,  in  the  mercury  lamp,  these  different  combinations  of  radia- 
tion may  not  give  the  same  resultant  any  more,  that  is,  become 
of  different  colors,  and  inversely,  different  colors,  which  differ 
only  by  such  component  radiations  as  are  blotted  out  by  an 
illuminant,  become  equal  in  this  illuminant.  For  instance,  a 
mixture  of  red  and  blue,  as  a  diluted  potassium  permanganate 
solution,  appears  violet  in  daylight.  In  the  mercury  light  it 
appears  blue,  as  the  red  is  blotted  out,  and  in  the  light  of  the 
incandescent  lamp  it  appears  red,  as  the  blue  is  blotted  out. 

I  show  you  here,  in  the  light  of  an  incandescent  lamp,  two 
pieces  of  black  velvet.  I  turn  off  the  incandescent  lamp  and 
turn  on  the  mercury  lamp,  and  you  see  the  one  piece  is  blue,  and 
the  other  black.  Now  I  show  you  two  pieces  of  brownish  black 
cloth  in  the  mercury  light.  Changing  to  the  incandescent  lamp 
you  see  that  the  one  is  a  bright  crimson,  and  the  other  still  practi- 
cally black.  In  both  cases  the  color  deficient  in  the  illuminant 
appeared  as  black. 

This  tube  of  copper  chloride  crystals  appears  bright  green  in 
the  incandescent  lamp.  In  the  mercury  light  it  is  a  dirty  white. 
The  excess  color,  green,  is  blotted  out. 

These  crystals  of  didymium  nitrate,  which  are  a  faint  light 
pink  in  daylight,  are  dark  pink  in  the  incandescent  light.  In 
the  mercury  light  they  are  blue :  the  color  is  a  mixture  of  red  and 
blue,  and  the  one  is  blotted  out  in  the  mercury  light  and  the  other 
in  the  incandescent  light. 

These  two  tubes,  one  containing  a  concentrated  solution  of 
manganese  chloride,  the  other  a  solution  of  didymium  nitrate,  are 
both  a  dark  pink  in  the  incandescent  light.  In  the  mercury 
light  the  first  becomes  a  very  faint  pink,  the  second  becomes  grass 
green. 

These  tubes,  one  containing  a  solution  of  didymium  nitrate,  the 
other  a  diluted  solution  of  nickel  sulphate,  appear  both  light  green 
in  the  mercury  light.  In  the  incandescent  lamp  the  former  is 
dark  pink,  the  latter  dark  green.  [Didymium,  which  formerly 
was  considered  as  an  element,  has  been  resolved  into  two  ele- 
ments, praseodymium,  which  gives  green  salts,  and  neodymium, 
which  gives  pink  salts.  It  is  interesting  to  see  that  this  separa- 


36  RADIATION,  LIGHT,  AND  ILLUMINATION. 

tion  is  carried  out  photometrically  by  the  light:  the  mercury 
lamp  showing  only  the  green  color  of  the  praseodymium,  the 
incandescent  lamp  the  pink  color  of  neodymium]. 

I  have  here  a  number  of  tubes,  which  seen  in  the  light  of 
the  incandescent  lamp  contain  red  solutions  of  nearly  the  same 
shade.  Changing  to  the  mercury  lamp  you  see  that  they  exhibit 
almost  any  color.  As  the  red  disappeared  in  the  mercury  lamp 
the  other  component  colors,  which  did  not  show  in  the  incandes- 
cent lamp  as  they  were  very  much  less  in  intensity  than  the  red, 
now  predominate :  potassium  permanganate  solution  turns  blue, 
carmine  blue ;  potassium  bichromate,  greenish  brown ;  coralline, 
(an  aniline  dye),  olive  green,  etc.,  etc. 

Again,  a  number  of  tubes,  which  in  the  mercury  light  appear  of 
the  same  or  nearly  the  same  blue  color,  turn  to  very  different 
colors  when  seen  in  the  incandescent  lamp,  due  to  the  appearance 
of  red  and  green,  which  were  not  seen  with  the  mercury  light. 

A  solution  of  rhodamine,  however,  which  looks  a  dull  red  in  the 
light  of  the  incandescent  lamp,  turns  a  glowing  crimson  in  the 
mercury  lamp,  due  to  its  red  fluorescence.  This  diluted  solution 
of  rhodamine  and  methyl  green  (aniline  dyes),  which  is  grey  in  the 
light  of  the  incandescent  lamp,  turns  brownish  red  in  the  mercury 
lamp,  the  green  is  blotted  out,  while  the  rhodamine  shows  its 
red  fluorescence.  Thus,  you  see,  the  already  very  difficult  prob- 
lem of  judging  the  subjective  colors  of  bodies  under  different  illu- 
minants  is  still  greatly  increased  by  phenomena  as  fluorescence. 

To  conclude  then :  we  have  to  distinguish  between  colorless  and 
colored  bodies,  between  opaque  colors  and  transparent  colors, 
between  color,  as  referred  to  the  visible  range  of  radiation  only, 
or  to  the  total  range,  including  ultra-red  and  ultra-violet,  and 
especially  we  have  to  realize  the  distinction  between  objective  or 
actual  color,  and  between  subjective  or  apparent  color,  when 
dealing  with  problems  of  illuminating  engineering. 


LECTURE  III. 
PHYSIOLOGICAL   EFFECTS   OF    RADIATION. 

Visibility. 

20.  The  most  important  physiological  effect  is  the  visibility  of 
the  narrow  range  of  radiation,  of  less  than  one  octave,  between 
wave  length  76  X  10~6  and  39  X  1Q-6. 

The  range  of  intensity  of  illumination,  over  which  the  eye  can 
see  with  practically  equal  comfort,  is  enormous:  the  average 
intensity  of  illumination  at  noon  of  a  sunny  day  is  nearly  one 
million  times  greater  than  the  illumination  given  by  the  full  moon, 
and  still  we  can  see  fairly  well  in  either  case;  that  is,  the  human 
eye  can  adapt  itself  to  enormous  differences  in  the  intensity  of 
illumination,  and  that  so  perfectly  that  it  is  difficult  to  realize  the 
differences  in  intensity  without  measuring  them.  The  photo- 
graphic camera  realizes  it.  An  exposure  taken  in  T^  second 
with  TV  opening  of  the  diaphragm  in  full  sunlight  usually  gives  a 
better  photograph  than  an  exposure  of  10  minutes  at  full  opening, 
in  the  light  of  the  full  moon.  The  ratio  of  time  of  exposure  in 
the  two  cases,  however,  is  about  1  to  1,000,000,  thus  showing  the 
difference  in  the  intensity  of  illumination.  Also,  the  disk  of  the 
moon,  when  seen  in  daylight,  has  about  the  same  intensity  as  the 
sky  —  somewhat  more  than  the  cloudless  sky,  less  than  white 
reflecting  clouds.  As  the  surface  of  the  moon's  disk,  of  one-half 
degree  diameter,  is  about  TffsWtf  the  surface  of  the  sky,  it  thus 
follows  that  the  daylight  reflected  from  the  sky  is  about  100,000 
times  more  intense  than  the  light  of  the  full  moon. 

The  organ  by  which  we  perceive  the  radiation,  the  human  eye 
(Fig.  20),  contains  all  the  elements  of  a  modern  photographic 
camera  —  an  achromatic  lense:  the  lense  L,  of  high  refractive 
power,  enclosed  between  the  two  transparent  liquids  A  and  B 
which  correct  the  color  dispersion,  that  is,  give  the  achromatic 
property;  a  diaphragm:  the  iris  7,  which  allows  the  increase  or 
decrease  of  the  opening  P,  the  pupil;  a  shutter:  the  eyelids  and 

87 


38  RADIATION,  LIGHT,  AND  ILLUMINATION 

the  sensitive  plate  or  retina  R.    The  nerves  of  vision  end  at  the 
back  of  the  retina,  and  in  the  center  of  the  retina  is  a  spot  F, 

the  "sensitive  spot "  or  "  fova,"  at  which 
the  retina  is  very  thin,  and  the  nerve 
ends  specially  plentiful.  At  this  spot  we 
thus  see  sharpest  and  clearest,  and  it  is 
this  spot  we  use  for  seeing  by  turning 
the  eye  so  as  to  fix  on  it  the  image  of 
the  subject  we  desire  to  see,  while  the 
image  on  the  rest  of  the  retina  is  used 
merely  for  orientation. 

The    adaptability    to    the   enormous 
FIG.  20.  range  of  intensity  of  illumination,  which 

as  seen  we  meet  in  nature,  is  secured: 

(1).  By  changing  the  opening  and  thereby  the  amount  of  light 
admitted  to  the  eye,  by  contracting  or  opening  the  pupil  P.  This 
action  is  automatic.  In  low  intensity  of  illumination  the  pupil 
thus  is  wide  open  and  contracts  at  higher  intensities.  As  this 
automatic  action  takes  an  appreciable,  though  short  time,  a  flash 
light  photograph  shows  the  pupil  of  the  eye  fully  open  and  thereby 
gives  a  staring  impression  to  the  faces  which  is  avoided  by  keep- 
ing a  photographically  inactive  light,  as  a  candle,  burning  outside 
of  the  field  of  the  camera  when  preparing  for  a  flash  light  photo- 
graph. 

(2).  By  the  fatigue  of  the  optic  nerves,  exposed  to  high  inten- 
sity of  illumination,  the  nerves  becomes  less  sensitive,  while  at 
low  intensity  they  rest  and  thus  become  more  sensitive,  and  the 
differences  of  sensation  are  hereby  made  very  much  less  than 
corresponds  to  the  differences  of  intensity  of  radiation.  There- 
fore, when  entering  a  brightly  illuminated  room  from  the  dark- 
ness we  are  blinded  in  the  first  moment,  until  the  eye  gets 
accustomed  to  the  light,  that  is,  the  nerves  become  fatigued  and 
so  reduce  the  sensation  of  light.  Inversely,  when  stepping  from 
a  bright  room  into  the  darkness  we  first  see  almost  nothing  until 
the  eye  gets  accustomed  to  the  darkness,  that  is,  the  nerves  of 
vision  are  rested  and  their  sensitivity  thus  increased  so  as  to  per- 
ceive the  much  lower  intensity  of  illumination. 

(3).  By  the  logarithmic  law  of  sensation.  The  impression  made 
on  our  senses,  eye,  ear,  etc.,  that  is,  the  sensation,  is  not  propor- 
tional to  the  energy  which  produces  the  sensation,  that  is,  the 


PHYSIOLOGICAL  EFFECTS  OF  RADIATION.  39 

intensity  of  the  light,  the  sound,  etc.,  but  is  approximately 
proportional  to  its  logarithm  and  the  sensation,  therefore, 
changes  very  much  less  than  the  intensity  of  light,  etc.,  which 
causes  the  sensation.  Thus  a  change  of  intensity  from  1  to 
1000  is  1000  times  as  great  a  change  of  intensity  as  from 
1  to  2,  but  the  change  of  sensation  in  the  first  case,  log  1000  =  3, 
is  only  about  10  times  as  great  as  the  change  in  the  latter  case, 
log  2  -  0.301. 

This  logarithmic  law  of  sensation  (Fechner's  Law),  while  usu- 
ally not  clearly  formulated,  is  fully  familiar  to  everybody,  is  con- 
tinuously used  in  life,  and  has  been  used  from  practical  experience 
since  by-gone  ages.  It  means  that  the  same  relative  or  percent- 
age change  in  intensity  of  light,  sound,  etc.,  gives  the  same  change 
of  sensation,  or  in  other  words,  doubling  the  intensity  gives  the 
same  change  in  sensation,  whether  it  is  a  change  of  intensity  from 
one  candle  power  to  two  candle  power,  or  from  10  to  20,  or  from 
1000  to  2000  candle  power. 

It  is  obvious  that  the  change  of  sensation  is  not  proportional  to 
the  change  of  intensity;  a  change  of  intensity  of  light  by  one 
candle  power  gives  a  very  marked  change  of  sensation,  if  it  is  a 
change  from  one  to  two  candle  power,  but  is  unnoticeable,  if  it  is  a 
change  from  100  to  101  candle  power.  The  change  of  sensation 
thus  is  not  proportional  to  the  absolute  change  of  intensity  —  one 
candle  power  in  either  case  —  but  to  the  relative  or  percentage 
change  of  intensity,  and  as  this  is  100  per  cent  in  the  first,  1  per 
cent  in  the  latter  case,  the  change  of  sensation  is  marked  in  the 
first,  unnoticeable  in  the  latter  case. 

This  law  of  sensation  we  continuously  rely  upon  in  practice. 
For  instance,  when  designing  an  electrical  distribution  system  for 
lighting,  we  consider  that  the  variation  of  voltage  by  1  per  cent  is 
permissible  as  it  gives  a  change  of  candle  power  of  about  5  per 
cent,  and  5  per  cent  variation  is  not  seriously  noticeable  to  the  eye. 
Now  this  5  per  cent  change  of  candle  power  may  be  a  change  from 
1  to  0.95,  or  by  -fa  candle  power,  or  it  may  be  a  change  from  1000 
to  950,  or  by  50  candle  power,  and  both  changes  we  assume,  and 
are  justified  herein  from  practical  experience,  to  give  the  same 
change  of  sensation,  that  is,  to  be  near  the  limits  of  permissi- 
bility. 

This  law  of  sensation  (Fechner's  Law)  means : 

If  i  =  intensity  of  illumination,  as  physical  quantity,  that  is, 


40  RADIATION,  LIGHT,  AND  ILLUMINATION. 

in  meter-candles  or  in  watts  radiation  of  specified  wave  length, 
the  physiological  effect  given  thereby  is : 

L  =  A  log  V 

%> 

where  A  is  a  proportionality  constant  (depending  on  the  physio- 
logical measure  of  L)  and  \  is  the  minimum  perceptible  value  of 
illumination  or  the  "threshold  value,"  below  which  sensation 
ceases. 

The  minimum  value  of  change  of  intensity  i,  which  is  still 
just  perceptible  to  the  average  human  eye,  is  1.6  per  cent.  This, 
then,  is  the  sensitivity  limit  of  the  human  eye  for  changes  of 
illumination. 

Obviously,  when  approaching  the  threshold  value  i0,  the  sensi- 
tivity of  the  eye  for  intensity  changes  decreases. 

The  result  of  this  law  of  sensation  is  that  the  physiological  effect 
is  not  proportional  to  the  physical  effect,  as  exerted,  for  instance, 
on  the  photographic  plate.  The  range  of  intensities  permissible 
on  the  same  photographic  plate,  therefore,  is  far  more  restricted. 
A  variation  of  illumination  within  the  field  of  vision  of  1  to  1000, 
as  between  the  ground  and  the  sky,  would  not  be  seriously  felt  by 
the  eye,  that  is,  not  give  a  very  great  difference  in  the  sensation. 
On  the  photographic  plate,  the  brighter  portions  would  show  1000 
times  more  effect  than  the  darker  portions  and  thus  give  bad 
halation  while  the  latter  are  still  under  exposed.  A  photographic 
plate,  therefore,  requires  much  smaller  variations  of  intensity  in 
the  field  of  vision  than  permissible  to  the  eye.  In  the  same  man- 
ner the  variations  of  intensity  of  the  voice,  used  in  speaking,  are 
far  beyond  the  range  of  impression  which  the  phonograph  cylin- 
der can  record,  and  when  speaking  into  the  phonograph  a  more 
uniform  intensity  of  the  voice  is  required  to  produce  the  record, 
otherwise  the  lower  portions  of  the  speech  are  not  recorded,  while 
at  the  louder  portions  the  recording  point  jumps  and  the  voice 
breaks  in  the  reproduction. 

21.  The  sensitivity  of  the  eye  to  radiation  obviously  changes 
with  the  frequency,  as  it  is  zero  in  the  ultra-red,  and  in  the  ultra- 
violet — where  the  radiation  is  not  visible  —  and  thus  gradually 
increases  from  zero  at  the  red  end  of  the  spectrum  to  a  maximum 
somewhere  near  the  middle  of  the  spectrum  and  then  decreases 
again  to  zero  at  the  violet  end  of  the  spectrum;  that  is,  the  physi- 


PHYSIOLOGICAL  EFFECTS  OF  RADIATION. 


41 


ological  effect  produced  by  the  same  radiation  power  —  as  one 
watt  of  radiating  power  —  is  a  maximum  near  the  middle  of  the 
visible  spectrum  and  decreases  to  zero  at  the  two  ends,  about  as 
illustrated  by  the  curves  in  Fig.  21.  Inversely,  the  mechanical 
equivalent  of  light,  or  the  power  required  to  produce  the  same 
physiological  effect  —  as  one  candle  power  of  light  —  is  a  maxi- 
mum near  the  middle  of  the  spectrum  and  decreases  from 
there  to  infinity  at  the  end  of  the  visible  range,  being  infinite 


RED 

YELLOW 

GREEN 

BLUE 

VIOLET 

FIG.  21. 

in  the  ultra-red  and  ultra-violet,  where  no  power  of  radiation  can 
produce  visibility.     It  thus  varies  about  as  indicated  in  Fig.  22. 

The  mechanical  power  equivalent  of  light,  thus,  is  not  constant, 
as  the  mechanical  energy  equivalent  of  heat  —  which  is  426  kgm. 
or  4.25  kile-joule  per  calorie  —  but  is  a  function  of  the  frequency, 
that  is,  of  the  color  of  radiation,  with  a  maximum,  probably  not 
very  far  from  0.01  watt  per  candle  power  in  the  middle  of  the 
spectrum. 

When  comparing,  however,  the  physiological  effects  of  different 
frequencies  of  radiation,  that  is,  different  colors  of  light,  the  diffi- 
culty arises  that  different  colored  lights  cannot  be  compared 
photometrically,  as  all  photometers  are  based  on  making  the  illu- 
mination produced  by  the  two  different  sources  of  light  equal,  and 
when  these  sources  of  light  are  of  different  color  they  can  never 
become  equal.  As  long  as  the  colors  are  not  very  different  - 
two  different  shades  of  yellow  or  yellowish  white  and  white  —  the 
eye  can  still  approximately  estimate  the  equality  of  intensity  and 


42 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


thus  compare  them,  though  not  as  accurately  as  when  the  two 
sources  of  light  are  of  the  same  color.  With  very  great  color 
differences,  as  green  light  and  orange  light,  this  is  no  longer 
feasible.  However,  an  accurate  comparison  can  still  be  made  on 
the  basis  of  equal  ease  in  distinguishing  objects.  As  the  pur- 


FIG.  22. 

pose  for  which  light  is  used  is  to  distinguish  objects,  the  correct 
comparison  of  lights  obviously  is  on  the  basis  of  equal  distinctness 
of  objects  illuminated  by  them;  that  is,  two  lights,  regardless 
whether  of  the  same  or  of  different  colors,  give  the  same  candle 
power,  that  is,  the  same  physiological  effect,  if  they  enable  us  to 
distinguish  objects  with  the  same  ease  at  the  same  distance. 
Experience  has  shown  that  the  sharpest  distinction,  that  is,  the 
greatest  accuracy  in  comparing  different  lights  in  this  manner,  is 
reached  by  determining  the  distance  from  the  source  of  light  at 


PHYSIOLOGICAL  EFFECTS  OF  RADIATION.  43 

which  print  of  moderate  size  just  ceases  to  be  readable.  For  this 
purpose  the  print  must  be  a  mixture  of  letters  which  do  not  form 
intelligible  words  and  the  point  which  can  be  determined  most 
accurately  is  where  large  letters,  as  capitals,  are  still  readable, 
while  small  letters  are  already  unreadable  (see  p.  174) .  Obviously, 
in  comparing  different  colors  of  light  the  object  must  be  colorless, 
that  is,  the  print  be  black  on  white.  This  method  of  comparison 
of  the  physiological  effect,  by  what  has  been  called  the  "lumino- 
meter,"  is  theoretically  the  most  correct,  as  it  is  independent  of 
the  color  of  light.  It  is,  however,  not  as  accurate  as  the  compari- 
son by  photometer,  and  thus  the  average  of  a  number  of  observa- 
tions must  be  used.  The  only  error  which  this  method  leaves  is 
that  due  to  the  difference  in  the  sensitivity  of  different  eyes,  that 
is,  due  to  the  differences  between  the  sensitivity  curves  (Fig.  21), 
and  this  in  most  cases  seems  to  be  very  small. 

22.  It  is  found,  however,  that  the  sensitivity  curve  for  different 
colors  of  radiation  is  a  function  of  the  intensity  of  radiation;  that 
is,  the  maximum  sensitivity  point  of  the  eye  is  not  at  a  definite 
frequency  or  wave  length,  but  varies  with  the  intensity  of  illumi- 
nation and  shifts  more  towards  the  red  end  of  the  spectrum  for 
high,  towards  the  violet  end  of  the  spectrum  for  low  intensity  of 
illumination,  and  for  illumination  of  very  high  intensity  the  maxi- 
mum physiological  effect  takes  place  in  the  yellow  light,  while  for 
very  low  intensity  of  illumination  it  occurs  in  the  bluish  green 
light;  that  is,  at  high  intensity  yellow  light  requires  less  power 
for  the  same  physiological  effect  than  any  other  color  of  light, 
while  for  low  intensity,  bluish  green  light  requires  less  power  for 
the  same  physiological  effect  than  any  other  color  of  light.  Thus, 
if  an  orange  yellow  light,  as  a  flame  carbon  arc,  and  a  bluish  green 
light,  as  a  mercury  lamp,  appear  of  the  same  intensity  from  the 
distance  of  100  feet,  by  going  nearer  to  the  lamps  the  orange 
yellow  appears  to  increase  more  rapidly  in  intensity  than  the 
bluish  green,  and  from  a  very  short  distance  the  former  appears 
glaring  bright,  while  the  latter  is  disappointing  by  not  showing 
anywhere  near  the  same  apparent  intensity.  Inversely,  when 
going  further  and  further  away  from  the  two  lamps  the  orange 
yellow  light  seems  to  fade  out  more  rapidly  than  the  bluish  green, 
and  has  practically  disappeared  while  the  bluish  green  is  still 
markedly  visible.  A  mercury  lamp,  therefore,  can  be  seen  from 
distances  from  which  a  much  brighter  yellow  flame  arc  is  practi- 


44 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


cally  invisible,  but  inversely,  from  a  very  short  distance  the 
yellow  light  appears  dazzling,  while  a  mercury  lamp  of  higher 
candle  power  appears  less  bright. 

Fig.  23  illustrates  the  change  of  sensitivity  with  intensity,  by 
approximate  curves  of  the  variation  of  the  relative  sensitivity  of 
the  average  human  eye  with  the  intensity  i  of  illumination  in 


v 


FIG.  23. 

meter  candles  (or  rather  log  i)  as  abscissas,  for  red  light,  wave 
length  65.0;  orange  yellow  light,  wave  length  59;  bluish  green 
light,  wave  length  50.5;  and  violet  light,  wave  length  45.0. 

As  seen  for  red  light  as  well  as  violet  light  —  the  two  ends  of 
the  visible  spectrum  —  the  sensitivity  is  low,  while  for  orange 
yellow  as  well  as  bluish  green  light  —  near  the  middle  of  the 
visible  range  —  the  sensitivity  is  high. 

For  bluish  green  light,  however,  the  sensitivity  is  high  at  low 
and  moderate  intensities  but  falls  off  for  high  intensities,  while 
for  orange  yellow  light  the  sensitivity  is  high  at  high  intensities 
and  falls  off  at  medium  and  low  intensities  and  ultimately  vanishes, 
that  is,  becomes  invisible  at  intensities  many  times  higher  than 
those  at  which  green  light  is  still  well  visible. 

Red  light  vanishes  from  visibility  still  earlier  than  orange  yel- 
low light,  while  violet  light  remains  visible  even  at  very  low 
intensities. 

The  vanishing  points  of  the  different  colors  of  light,  that  is, 


PHYSIOLOGICAL  EFFECTS  OF  RADIATION.  45 

the  minimum  intensities  which  can  just  be  perceived  are,  approxi- 
mately, at: 

Color red      orange  yellow  green  blue  violet 

Wave  length  lw  =        67        60.5  57.5  50.5  47  .      43   x  10~fl 

Meter-candles  in- 
tensity ....  i0  =  0.06  0.0056  0.0029  0.00017  0.00012  0.00012 

Relative  radiation 

power po  =  10,000  1000  100  1  2  20 

That  is,  the  minimum  visible  amount  of  green  light  represents 
the  least  amount  of  power;  the  minimum  visible  amount  of 
blue  light  requires  twice  as  much  power  as  green  light;  violet 
light  20  times  as  much,  but  yellow  light  100  times  and  red  light 
even  10,000  times  as  much  power  as  green  light  at  the  threshold 
of  visibility. 

While  the  intensity  of  radiation  varies  inversely  proportional 
to  the  square  of  the  distance,  it  follows  herefrom  that  the  physio- 
logical effect  of  radiation  does  not  vary  exactly  with  the  square 
of  the  distance,  but  varies  somewhat  faster,  that  is,  with  a  higher 
power  of  the  distance  for  orange  yellow  or  the  long-wave  end  of 
the  spectrum,  and  somewhat  slower,  that  is,  with  a  lesser  power 
of  the  distance  than  the  square,  for  bluish  green  or  the  short-wave 
end  of  the  spectrum. 

This  phenomenon  is  appreciable  even  when  comparing  the 
enclosed  alternating  carbon  arc  with  the  open  direct  current  car- 
bon arc :  by  photometer,  where  a  fairly  high  intensity  of  illumi- 
nation is  used,  the  relative  intensity  of  the  two  arcs  is  found 
somewhat  different  than  by  luminometer,  that  is,  by  reading 
distances  nearer  the  lower  limit  of  visibility.  For  low  intensities, 
the  alternating  arc  compares  more  favorably  than  for  high 
intensities. 

It  follows,  therefore,  that  in  the  photometric  comparison  of 
illuminants,  where  appreciable  color  differences  exist,  the  inten- 
sity of  illumination  at  which  the  comparison  is  made  must  be 
given,  as  it  influences  the  result,  or  the  candle  power  and  the 
distance  of  observation  stated. 

23.  Not  only  the  sensitivity  maximum  is  different  for  low  and 
for  high  intensity  of  illumination,  but  the  shape  of  the  sensi- 
tivity curve  also  is  altered,  and  for  low  intensity  is  more  peaked, 
that  is,  the  sensitivity  decreases  more  rapidly  from  a  maximum 
towards  the  ends-  of  the  spectrum  than  it  does  for  high  intensity 


46 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


of  illumination  as  indicated  by  the  curves  in  Fig.  24  which 
shows  approximate  sensitivity  curves  of  the  average  human  eye : 
(a)  for  every  low  illumination  near  the  treshold  value  of  visi- 
bility or  0.001  meter-candles;  (b)  for  medium  illumination,  4.6 
meter-candles;  (c)  for  very  high  illumination,  600  meter-candles. 


lu,*-.    1.65 
I     =      45.0 


1.70 
50.0 


L 


t 


\ 


\ 


\ 


FIG.  24. 


(1  meter-candle  is  the  illumination  produced  by  1  candle  power 
of  light  intensity  at  1  meter  distance;  N  meter-candles,  thus,  the 
illumination  produced  by  a  light  source  of  N  candle  power  at  1 

meter  distance  or  of  1  candle  power  at— -=  meter  distance,  etc.). 

VN 

As  seen,  curve  (a)  ends  at  wave  length  /„,  =  61  X  10~fl;  that  is, 
for  longer  waves  or  orange  and  red  light,  0.001  meter-candles  is 
below  the  threshold  value  of  visibility,  hence  is  no  longer  visible. 

The  maximum  visibility,  that  is  the  sensitivity  maximum  of 
the  human  eye,  lies  at  wave  length. 

Z0  =  51.1,  bluish  green  for  very  low  intensity,  curve  (a). 
Z0  =  53.7,  yellowish  green  for  medium  intensity,  curve  (b). 
10  =  56.5,  yellow  for  high  intensity,  curve  (c). 

The  sensitivity  maximum  varies  with  the  intensity  about  as 
shown  in  Fig.  25;  that  is,  it  is  constant  in  the  bluish  green  for 
low  intensities,  changes  at  medium  intensities  in  the  range  be- 
tween 0.5  and  50  meter-candles  and  again  remains  constant  in 
the  yellow  for  still  higher  intensities. 


PHYSIOLOGICAL  EFFECTS  OF  RADIATION. 


47 


The  sensitivity  curves,  as  given  in  Fig.  24,  have  the  general 
character  of  probability  curves : 


where  lwo  is  the  wave  length  at  maximum  sensitivity  and  HQ  is 
the  sensitivity  at  this  wave  length,  that  is,  the  maximum  sensi- 
tivity and  ks  is  a  constant  which  is  approximately  120  for  low, 


LOG 

t=      - 

3 

I2 

- 

1 

0 

* 

1 

+ 

a 

4 

3    57 

-    0. 

X)l 

0. 

bi 

0 

i 

1 

1 

1 

^1 

)0 

100 

^x 

ME 

s 

ER-C, 

NDLE 

'/ 

';\ 

V 

/ 

/ 

Sr, 

H=H< 

«•*• 

(j*~ 

i)2 

^s 

>c 

*~-     , 

/ 

[gg 

S 

FIG.  25. 

62  for  high  intensities  and  changes  in  approximately  the  same 
range  of  intensities  in  which  lwo  changes;  ks  is  also  plotted  in 
Fig.  25. 

This  effect  of  the  intensity  of  illumination  on  the  sensitivity  of 
the  eye  is  very  important  in  illuminating  engineering  as  it  deter- 
mines the  color  shades  which  are  most  effective  for  the  particular 
purpose.  For  instance,  in  sending  the  light  to  great  distances, 
for  signalling,  etc.,  the  bluish  green  of  the  mercury  lamp  is  best 
suited,  carries  farthest,  and  the  yellow  flame  arc  the  poorest;  the 
white  carbon  arc  superior  to  the  yellow  flame  arc,  even  where  the 
latter  is  of  greater  intensity.  Inversely,  where  a  big  glare  of 
light  is  desired,  as  for  decorative  purposes,  for  advertising,  etc., 
the  yellow  flame  carbon  arc  is  best  suited,  the  bluish  green  mer- 
cury lamp  disappointing. 

Apparent  exceptions  may  exist :  for  instance,  the  long  waves  of 
the  orange  yellow  penetrate  fog  better  than  the  short  waves  of 
bluish  green,  and  for  lighthouses,  where  the  important  problem  is 
to  reach  the  greatest  possible  distance  in  fog,  yellow  light,  thus, 
may  be  superior.  In  general,  however,  the  bluish  green  is  superior 


48  RADIATION,  LIGHT,  AND  ILLUMINATION. 

in  visibility  to  the  orange  yellow  for  long  distances,  and  inversely, 
the  orange  yellow  is  superior  for  short  distances. 

At  the  limits  of  visibility  the  eye  is  very  many  times  more 
sensitive  to  green  light  and,  in  general,  high-frequency  light,  than 
to  orange  yellow  and,  in  general,  low-frequency  light. 

A  necessary  result  of  the  higher  sensitivity  of  the  eye  for  green 
light  is  the  preponderance  of  green  in  gas  and  vapor  spectra.  As 
no  special  reason  exists  why  spectrum  lines  should  appear  more 
frequently  at  one  wave  length  than  at  any  other  and  as  the  radia- 
tion is  most  visible  in  the  green,  this  explains,  somewhat,  the 
tendency  of  most  highly  efficient  illuminants  towards  a  greenish 
or  yellow  color  (as,  for  instance,  the  Welsbach  mantel,  the  Nernst 
lamp,  etc.). 

Pathological  and  Other  Effects  on  the  Eye. 

24.  Radiation  is  a  form  of  energy,  and  thus,  when  intercepted 
and  absorbed,  disappears  as  radiation  by  conversion  into  another 
form  of  energy,  usually  heat.  Thus  the  light  which  enters  the 
eye  is  converted  into  heat,  and  if  its  power  is  considerable  it  may 
be  harmful  or  even  destructive,  causing  inflammation  or  burns. 
This  harmful  effect  of  excessive  radiation  is  not  incident  to  any 
particular  frequency,  but  inherent  in  radiation  as  a  form  of 
energy.  It  is,  therefore,  greatest  for  the  same  physiological  effect, 
that  is,  the  same  amount  of  visibility,  for  those  frequencies  of 
light  which  have  the  lowest  visibility  or  highest  power  equiva- 
lent, that  is,  for  the  red  and  the  violet  and  least  for  the  green  and 
the  yellow,  which  for  the  same  amount  of  visibility  represent 
least  power.  Hence,  green  and  greenish  yellow  light  are  the  most 
harmless,  the  least  irritating  to  the  eye,  as  they  represent  the 
least  power.  We  feel  this  effect  and  express  it  by  speaking  of 
the  green  light  as  "cold  light"  and  of  the  red  and  orange  light  as 
"hot"  or  "warm."  The  harmful  effect  of  working  very  much 
under  artificial  illumination  is  largely  due  to  this  energy  effect, 
incident  to  the  large  amount  of  orange,  red,  and  especially  ultra- 
red  in  the  radiation  of  the  incandescent  bodies  used  for  illumi- 
nants and  thus  does  not  exist  with  "cold  light,"  as  the  light  of 
the  mercury  lamp. 

Blue  and  violet  light,  however,  are  just  as  energetic,  or  "hot," 
as  orange  and  red  light,  and  the  reason  that  they  are  usually  not 
recognized  as  such  is  that  we  have  no  means  to  produce  efficiently 


PHYSIOLOGICAL  EFFECTS  OF  RADIATION. 


49 


powerful  blue  and  violet  light,  and  if  we  could  produce  it  would 
not  be  able  to  use  it  for  illumination,  due  to  the  specific  effects  of 
this  light  which  will  be  described  in  the  following. 

If,  in  Fig.  26,  the  curve  A  represents  roughly  the  mechanical 
power  equivalent  of  light  for  average  intensity,  that  is,  the  power 
required  to  produce  the  same  physiological  effect  or  the  same 
candle  power,  the  distribution  of  power  in  an  incandescent  lamp 


YELLOW  GREEN 

FIG.  26. 


carbon  filament  would  be  somewhat  like  C.  That  is,  the  physio- 
logical effect  falls  off  somewhat  towards  the  green,  as  C  drops 
more  than  A,  and  almost  vanishes  in  the  blue  and  violet,  as  C 
rapidly  decreases,  while  A,  the  power  required  to  give  the  same 
physiological  effect,  rapidly  increases.  From  the  yellow  towards 
the  red  the  physiological  effect  again  decreases  somewhat,  but 


50  RADIATION,  LIGHT,  AND  ILLUMINATION. 

the  radiation  still  increases  towards  the  ultra-red.  Dividing  C 
by  A  then  gives  the  distribution  of  the  physiological  effect,  curve 
C',  that  is,  of  visibility,  in  the  incandescent  lamp  spectrum,  show- 
ing that  the  color  of  the  light  is  yellow.  Hg  gives  the  distribu- 
tion of  power  in  the  mercury  spectrum.  It  is  shown  in  dotted 
lines,  as  the  distribution  is  not  continuous,  but  the  power  massed 
at  definite  points,  the  spectrum  lines  of  mercury.  Hg'  then  gives 
the  visibility  curve  by  dividing  Hg  by  A.  As  seen,  the  ratio  of 
the  area  of  Hg*  to  Hg,  that  is,  the  ratio  of  the  physiological  effect 
to  the  power,  is  much  less  than  the  ratio  of  the  area  of  C'  to  C; 
that  is,  the  former  produces  for  the  same  amount  of  visibility  far 
less  heat  and  thus  is  safer. 

25.  Excessive  intensity,  such  as  produced  at  a  short-circuiting 
arc,  is  harmful  to  the  eye.  The  human  organism  has  by  evolu- 
tion, by  natural  selection,  developed  a  protective  mechanism 
against  the  entrance  of  radiation  of  excessive  power  into  the  eye : 
at  high  intensity  of  illumination  the  pupil  of  the  eye  contracts 
and  thus  reduces  the  amount  of  light  admitted,  and  a  sudden 
exposure  to  excessive  radiation  causes  the  eyelids  to  close.  This 
protective  mechanism  is  automatic;  it  is,  however,  responsive 
mainly  to  long  waves  of  radiation,  to  the  red  and  the  yellow  light, 
but  not  to  the  short  waves  of  green,  blue  and  violet  light.  The 
reason  for  this  is  apparently  that  all  sources  of  excessive  radia- 
tion which  are  found  in  nature,  the  sun  and  the  fire,  are  rich  in 
red  and  yellow  rays,  but  frequently  poor  in  rays  of  short  wave 
length,  and,  therefore,  a  response  to  short  wave  lengths  alone  would 
not  be  sufficient  for  protection  as  they  might  be  absent  in  many 
intense  radiations,  while  a  response  to  long  waves  would  be 
sufficient  since  these  are  always  plentiful  in  the  intense  radiations 
found  in  nature. 

It  is  only  of  late  years  that  illuminants,  as  the  mercury  lamp, 
which  are  deficient  in  the  long  waves,  have  been  produced,  and  for 
these  the  protective  action  of  the  eye,  by  contracting  the  pupil, 
fails.  This  absence  or  reduction  of  the  contraction  of  the  pupil 
of  the  eye  in  the  light  of  the  mercury  lamp  is  noticed  when  passing 
from  a  room  well  illuminated  by  incandescent  lamps,  to  one  equally 
well  illuminated  by  mercury  lamps  and  inversely.  When  changing 
from  the  incandescent  light  to  the  mercury  light,  the  illumination 
given  by  the  latter  at  first  appears  dull  and  inferior  as  the  pupil 
is  still  contracted,  but  gradually  gains  in  intensity  as  the  pupil 


PHYSIOLOGICAL  EFFECTS  OF  RADIATION.  51 

opens;  and  inversely,  coming  from  the  mercury  light  to  the  incan- 
descent light,  the  latter  first  appears  as  a  big  glare  of  light,  the 
pupil  still  being  open,  but  gradually  dulls  down  by  the  contraction 
of  the  pupil. 

This  absence  of  the  automatic  protective  action  of  the  eye 
against  light  deficient  in  long  waves  is  very  important,  as  it  means 
that  exposure  to  excessive  intensity  of  illumination  by  mercury 
light  may  be  harmful,  due  to  the  power  of  the  light,  against  which 
the  eye  fails  to  protect,  while  the  same  or  even  greater  power  of 
radiation  in  yellow  light  would  be  harmless,  as  the  eye  will  pro- 
tect itself  against  it.  The  mercury  lamp,  therefore,  is  the  safest 
illuminant,  when  of  that  moderate  intensity  required  for  good 
illumination,  but  becomes  harmful  when  of  excessive  intensity,  as 
when  closely  looking  at  the  lamp  for  considerable  time,  when 
operating  at  excessive  current.  The  possibility  of  a  harmful 
effect  is  noticed  by  the  light  appearing  as  glaring.  This  phe- 
nomenon explains  the  contradictory  statements  occasionally  made 
regarding  the  physiological  effect  of  such  illuminants. 

26.  Up  to  and  including  the  green  light,  no  specific  effects, 
that  is,  effects  besides  those  due  to  the  power  of  radiation,  seem 
yet  to  exist.  They  begin,  however,  at  the  wave  length  of  blue 
light. 

I  show  you  here  a  fairly  intense  blue  violet  light,  that  is,  light 
containing  only  blue  and  violet  radiation.  It  is  derived  from  a 
vertical  mercury  lamp,  which  is  surrounded  by  two  concentric 
glass  cylinders  welded  together  at  the  bottom.  The  space  be- 
tween the  cylinders  is  filled  with  a  fairly  concentrated  solution 
of  potassium  permanganate  (strong  copper  nitrate  solution  or  a 
cupric-ammon  salt  solution,  though  not  quite  so  good  may  also 
be  used)  which  is  opaque  to  all  but  the  blue  and  violet  radiations. 
As  you  see,  the  light  has  a  very  weird  and  uncanny  effect,  is 
extremely  irritating:  you  can  see  by  it  as  the  intensity  of  illumi- 
nation is  fairly  high,  but  you  cannot  distinguish  everything,  and 
especially  the  lamp  is  indefinite  and  hazy :  you  see  it,  but  when 
you  look  at  it  it  disappears,  and  thus  your  eye  is  constantly  try- 
ing to  look  at  it  and  still  never  succeeds,  which  produces  an 
irritating  restlessness.  It  can  well  be  believed  that  long  exposure 
to  such  illumination  would  result  in  insanity.  The  cause  of  this 
weird  effect  —  which  is  difficult  to  describe  —  is  that  the  sensitive 
spot  on  the  retina,  that  is,  the  point  on  which  we  focus  the  image 


52  RADIATION,  LIGHT,  AND  ILLUMINATION. 

of  the  object  which  we  desire  to  see,  or  the  fova  F  in  Fig.  19,  is 
blue  blind,  that  is,  does  not  see  the  blue  or  violet  light.  Thus  we 
see  the  lamp  and  other  objects  indistinctly  on  the  outer  range  of 
the  retina,  but  what  we  try  to  see  distinctly  disappears  when 
focused  on  the  blue  blind  spot  F.  This  spot,  therefore,  is  often 
called  the  " yellow  spot,"  as  we  see  yellow  on  it  —  due  to  the 
absence  of  the  vision  of  blue  at  this  particular  place  of  the  retina. 

To  produce  this  effect  requires  the  mercury  lamp;  most  other 
illuminants  do  not  have  sufficient  blue  and  violet  rays  to  give 
considerable  illumination  of  this  color  and  even  if  they  do,  no 
screen  which  passes  blue  and  violet  is  sufficiently  opaque  to  the 
long  waves  not  to  pass  enough  of  them  to  spoil  the  effect,  if  the 
illuminant  is  rich  in  such  long  waves.  The  mercury  lamp,  how- 
ever, is  deficient  in  these,  and  thus  it  is  necessary  only  to  blind  off 
the  green  and  yellow  rays  in  order  to  get  the  blue  and  violet  light. 

I  show  you  here  a  mercury  lamp  enclosed  by  a  screen  consist- 
ing of  a  solution  of  naphtol  green  (an  aniline  dye)  which  transmits 
only  the  green  light.  As  you  see,  in  the  green  the  above-described 
effect  does  not  exist,  but  the  vision  is  clear,  distinct  and  restful. 

27.  Beyond  the  violet  the  radiation  is  no  longer  visible  to  the 
eye  as  light.  There  is,  however,  a  faint  perception  of  ultra-violet 
light  in  the  eye,  not  as  distinct  light,  but  rather  as  an  indis- 
tinct, uncomfortable  feeling,  some  form  of  dull  pain,  possibly 
resulting  from  fluorescence  effects  caused  by  the  ultra-violet 
radiation  inside  of  the  eye.  With  some  practice  the  presence  of 
ultra-violet  radiation  thus  can  be  noticed  by  the  eye  and  such 
light  avoided.  In  the  ultra-violet,  and  possibly  to  a  very  slight 
extent  in  the  violet  and  even  in  the  blue,  a  specific  harmful  effect 
appears,  which  probably  is  of  chemical  nature,  a  destruction  by 
chemical  dissociation.  This  effect  increases  in  severity  the 
further  we  reach  into  the  ultra-violet,  and  probably  becomes  a 
maximum  in  the  range  from  one  to  two  octaves  beyond  the  violet. 
These  very  short  ultra-violet  rays  are  extremely  destructive  to 
the  eye :  exposure  even  to  a  moderate  intensity  of  them  for  very 
few  minutes  produces  a  severe  and  painful  inflammation,  the 
after  effects  of  which  last  for  years,  and  long  exposures  would 
probably  result  in  blindness.  The  chronic  effects  of  this  inflam- 
mation are  similar  to  the  effect  observed  in  blue  light :  inability 
or  difficulty  in  fixing  objects  on  the  sensitive  spot  F,  so  that  with- 
out impairment  of  the  vision  on  the  rest  of  the  retina  clear  dis- 


PHYSIOLOGICAL  EFFECTS  OF  RADIATION.  53 

tinction  is  impaired  and  reading  becomes  difficult  or  impossible, 
especially  in  artificial  illumination.  It  appears  as  if  the  sensitive 
spot  F,  or  the  focusing  mechanism  of  the  eye,  were  over-irritated 
and  when  used,  for  instance  in  reading,  becomes  very  rapidly 
fatigued  and  the  vision  begins  to  blur.  If  further  irritation  by 
ultra-violet  light  or  by  attempting  to  read,  etc.,  is  avoided, 
gradually  the  rapidity  of  fatigue  decreases,  the  vision  remains 
distinct  for  a  longer  and  longer  time  before  it  begins  to  blur  and 
ultimately  becomes  normal  again. 

The  inflammation  of  the  eye  produced  by  ultra-violet  light 
appears  to  be  different  from  that  caused  by  exposure  to  high- 
power  radiation  of  no  specific  effect,  as  the  light  of  a  short  circuit 
of  a  high-power  electric  system,  or  an  explosion,  etc. 

The  main  differences  are: 

1.  The  effect  of  high-power  radiation  (power  burn)  appears 
immediately  after  exposure,  while  that  of  ultra-violet  radiation 
(ultra-violet  burn)  appears  from  6  to  18  hours  after  exposure. 

2.  The  external  symptoms  of  inflammation:    redness  of  the 
eyes  and  the  face,  swelling,  copious  tears,  etc.,  are  pronounced 
in  the  power  burn,  but  very  moderate  or  even  entirely  absent 
in  the  ultra-violet  burn. 

3.  Complete  recovery  from  a  power  burn  even  in  severe  cases 
usually  occurs  within  a  few  days,  leaving  no  after  effects,  while 
recovery  from  an  ultra-violet  burn  is  extremely  slow,  taking 
months  or  years,  and  some  after  effects,  as  abnormal  sensitivity 
to  radiation  of  short  wave  lengths,  may  be  practically  permanent. 

The  general  phenomena  of  a  severe  power  burn  are : 

Temporary  blindness  immediately  after  exposure,  severe  pains 
in  the  eyes  and  the  face,  redness  of  eyes  and  face,  swelling,  copi- 
ous tears,  etc.  These  effects  increase  for  a  few  hours  and  then 
decrease,  yielding  readily  to  proper  treatment:  application  of 
ice,  cold  boric  acid  solution,  etc.,  and  complete  recovery  occurs 
within  a  few  days. 

In  chronic  cases,  as  excessive  work  under  artificial  illumination, 
the  symptoms  appear  gradually,  but  recovery,  if  no  structural 
changes  in  the  eyes  have  occurred,  is  rapid  and  complete  by 
proper  treatment  and  discontinuance  of  work  under  artificial 
illumination. 

Most  artificial  light  is  given  by  temperature  radiation  (incan- 
descent lamp,  gas  and  kerosene  flame), and  therefore  its  radiation 


54  RADIATION,  LIGHT,  AND  ILLUMINATION. 

consists  of  a  very  small  percentage  only  of  visible  light  (usually 
less  than  1  per  cent),  while  most  of  its  energy  is  in  the  ultra-red 
and  invisible,  and  for  the  same  amount  of  visible  radiation  or 
light  the  total  radiated  power  thus  is  many  times  greater  than 
with  daylight.  Regarding  chronic  " power  burn,"  artificial  light, 
therefore,  is  much  more  harmful  than  daylight,  that  is,  much 
more  energy  enters  the  eye  under  incandescent  illumination  than 
under  much  more  powerful  daylight  illumination. 

In  a  severe  ultra-violet  burn  no  immediate  symptoms  are 
noticeable,  except  that  the  light  may  appear  uncomfortable 
while  looking  at  it.  The  onset  of  the  symptoms  is  from  6  to  18 
hours  later,  that  is,  usually  during  the  night  following  the  ex- 
posure, by  severe  deep-seated  pains  in  the  eyes;  the  external 
appearance  of  inflammation  is  moderate  or  absent,  the  vision  is 
not  impaired,  but  distinction  made  difficult  by  the  inability  to 
focus  the  eye  on  any  object.  The  pains  in  the  eyes  and  head- 
ache yield  very  slowly;  for  weeks  and  even  months  any  attempt 
of  the  patient  to  use  the  eyes  for  reading,  or  otherwise  sharply 
distinguishing  objects,  leads  to  blurring  of  the  vision;  the  letters 
of  the  print  seem  to  run  around  and  the  eye  cannot  hold  on 
to  them,  and  severe  headache  and  deep-seated  pains  in  the 
eyes  follow  such  attempt.  Gradually  these  effects  become  less; 
after  some  months  reading  for  a  moderate  length  of  time  during 
daylight  is  possible,  but  when  continued  too  long,  or  in  poor 
light,  as  in  artificial  illumination,  leads  to  blurring  of  the  vision 
and  head  or  eye  ache.  Practically  complete  recovery  occurs 
only  after  some  years,  and  even  then  some  care  is  necessary,  as 
any  very  severe  and  extended  strain  on  the  eyes  temporarily 
brings  back  the  symptoms.  Especially  is  this  the  case  when 
looking  at  a  light  of  short  wave  length,  as  the  mercury  arc;  that 
is,  there  remains  an  abnormal  sensitivity  of  the  eye  to  light  of 
short  wave  lengths,  even  such  light  which  to  the  normal  eye  is 
perfectly  harmless,  as  the  mercury  lamp. 

In  chronic  cases  of  ultra-violet  burn,  which  may  occur  when 
working  on  unprotected  arcs,  and  especially  spark  discharges 
(as  in  wireless  telegraphy),  the  first  symptoms  are:  occasional 
headaches,  located  back  of  the  eyes,  that  is,  pains  which  may 
be  characterized  either  as  headache  or  as  deep-seated  eye  ache. 
These  recur  with  increasing  frequency  and  severity.  At  the 
same  time  the  blurring  of  the  vision  begins  to  be  noticeable 


PHYSIOLOGICAL  EFFECTS  OF  RADIATION.  55 

and  the  patient  finds  it  more  and  more  difficult  to  keep  the  eye 
focused  for  any  length  of  time  on  objects,  as  the  print  when  read- 
ing. These  symptoms  increase  m  severity  until  the  patient 
is  obliged  to  give  up  the  occupation  which  exposed  him  to  ultra- 
violet light,  and  then  gradual  recovery  occurs,  as  described  above, 
if  the  damage  has  not  progressed  too  far. 

In  mild  cases  recovery  from  power  burns  may  occur  in  a  few 
hours  and  complete  recovery  from  mild  ultra-violet  burns  in 
a  few  weeks. 

Both  types  of  burn  may  occasionally  occur  simultaneously 
and  their  symptoms  then  successively. 

For  instance,  in  a  case  of  an  exposure  while  working  for  about 
half  an  hour  with  a  flame-carbon  arc  without  enclosing  glass 
globe  (such  an  arc  contains  large  amounts  of  high-power  radia- 
tion, of  yellow  and  orange  color,  but  also  a  considerable  amount 
of  ultra-violet  rays),  the  symptoms  of  the  power  burn  increased 
in  severity  for  a  few  hours,  and  then  rapidly  vanished  by  the 
application  of  cold  water,  and  recovery  was  practically  complete 
six  hours  after  exposure;  then  some  hours  later,  in  the  middle 
of  the  night,  the  patient  was  awakened  by  severe  pains  in  the 
eyes,  the  symptoms  of  the  ultra-violet  burn,  and  had  to  seek 
medical  attendance.  Under  proper  treatment  recovery  occurred 
in  a  few  days,  but  the  blurring  of  the  vision  was  appreciable 
for  some  days  longer,  and  the  sensitivity  to  high-frequency  light 
for  some  weeks. 

28.  Arcs  produce  considerable  amount  of  ultra-violet  light,* 
and  in  former  experiments  we  have  used  a  high  frequency  iron 
arc  for  producing  ultra-violet  light  and  also  have  seen  that  even  a 
very  thin  sheet  of  glass  is  opaque  for  these  radiations.  For  very 
long  ultra-violet  rays,  that  is,  the  range  close  to  the  visible  violet, 
glass  is  not  quite  opaque,  but  becomes  perfectly  opaque  for  about 
one-quarter  to  one-half  octave  beyond  the  violet,  and  in  this  first 
quarter  of  an  octave  the  harmful  effect  of  the  ultra-violet  radia- 
tion is  still  very  small  and  becomes  serious  only  when  approach- 
ing a  distance  of  about  one  octave  from  the  visible  end  of  the 
violet.  Clear  transparent  glass  thus  offers  a  practically  complete 
protection  against  the  harmful  effects  of  ultra-violet  light,  except 
when  the  latter  is  of  excessive  intensity,  and  thus  arcs  enclosed 

*  An  arc  between  silicon  terminals  emits  especially  powerful  ultra-violet 
radiation  accompanied  by  little  visible  light. 


56  RADIATION,  LIGHT,  AND  ILLUMINATION. 

by  glass  globes  are  harmless.  It  is,  however,  not  safe  to  look 
into  and  work  in  the  light  of  open  metal  arcs  for  too  long  a 
time. 

The  carbon  arc  gives  the  least  ultra-violet  rays,  so  little  that 
even  without  enclosure  by  glass  it  is  fairly  safe;  metal  arcs  give 
more  and  the  mercury  arc  gives  the  greatest  amount  and  reaches 
to  the  farthest  distance  beyond  the  visible,  and  these  very  destruc- 
tive very  short  ultra-violet  rays  have  so  far  only  been  observed  in 
the  radiation  of  a  low  temperature  mercury  arc  in  a  quartz  tube : 
quartz  being  transparent  to  these  rays  while  glass  is  opaque. 
The  high  temperature  mercury  arc  in  a  quartz  tube,  that  is,  arc 
operated  near  atmospheric  pressure  as  it  is  used  to  some  extent 
for  illumination,  especially  abroad,  seems  to  be  much  less  dan- 
gerous than  the  low  temperature  or  vacuum  arc,  but  it  also 
requires  a  protecting  glass  globe. 

In  general,  no  metal  arc,  spark  discharge,  or  glow  discharge 
should  ever  be  used  industrially  or  otherwise  without  being  en- 
closed by  a  glass  globe,  preferably  of  lead  glass,  if  located  so  that 
it  may  be  looked  at.  Those  experimenting  with  arcs  or  other 
electric  discharges  should  always  protect  their  eyes  by  the  inter- 
position of  a  glass  plate. 

Thus  the  sparks  of  wireless  telegraph  stations,  the  discharges 
of  ozonizers,  the  arcs  of  nitric  acid  generators,  electric  furnaces, 
etc.,  may  be  dangerous  without  glass  enclosure. 

While  artificial  illuminants,  and  especially  metal  arcs,  give 
an  appreciable  amount  of  ultra-violet  light,  these  ultra-violet 
rays  extend  only  to  about  one-quarter  octave  beyond  the  visible 
violet  and  if,  as  is  always  the  case,  the  illuminant  is  enclosed  by 
glass,  the  harmful  effect  of  these  long  ultra-violet  rays  is  negli- 
gible. The  radiation  of  the  sun  also  contains  ultra-violet  rays, 
and  a  larger  percentage  compared  with  the  total  radiation  than 
any  glass-enclosed  artificial  illuminant,  and  as  the  light  of  the  sun, 
that  is,  daylight,  is  recognized  as  perfectly  harmless,  as  far  as 
this  specific  destructive  action  is  concerned,  the  same  applies  to 
the  artificial  illuminants,  as  they  contain  less  ultra-violet  rays 
than  the  light  of  the  sun. 

This  specific  destructive  action  on  the  eye  of  short  ultra-violet 
radiation  extends  beyond  the  blank  space  in  the  spectrum  of 
radiation  (Fig.  14)  and  still  exists,  though  possibly  to  a  lesser 
extent,  in  the  X-rays. 


PHYSIOLOGICAL  EFFECTS  OF  RADIATION.  57 

Pathological  and  Therapeutic  Effects  of  Radiation. 

29.  Radiation  impinging  on  the  tissue  of  the  human  body 
or  other  living  organisms  exerts  an  influence  depending  on 
intensity,  power  and  frequency.  The  effect  on  the  eye  has  been 
discussed  in  the  preceding  paragraphs.  The  specific  chemical 
effect  in  supplying  the  energy  of  plant  life  will  be  more  fully 
discussed  in  the  following  under  chemical  effects.  As  is  to  be 
expected,  the  effect  of  radiation  on  the  living  protoplasm 
of  the  cells  is  stimulating  if  of  moderate  intensity,  destructive 
if  of  excessive  intensity;  that  is,  by  the  energy  of  the  radiation 
the  motions  of  the  parts  of  the  protoplasm-molecule  are  in- 
creased, and,  if  the  intensity  of  radiation  is  too  high,  the  mole- 
cule thus  is  torn  asunder,  that  is,  destroyed,  the  living  cell 
killed  and  inflammation  and  necrosis  (mortification)  result. 
If  the  intensity  is  moderate,  merely  an  increase  of  the  rapidity 
of  the  chemical  changes  in  the  protoplasm,  which  we  call  life, 
results;  that  is,  the  radiation  exerts  a  stimulating  effect,  in- 
creasing the  intensity  of  life,  causing  an  increased  renewal  of 
worn-out  tissue  and  reconstruction,  and  thus  is  beneficial  or 
curative,  especially  where  the  metabolism  is  sluggish. 

Just  as  in  the  action  on  the  eye,  two  different  effects  probably 
exist :  a  general  effect  due  to  the  energy  of  the  radiation  —  which 
with  sunlight  is  a  maximum  beyond  the  visible  close  to  the  red 
end  of  the  spectrum,  and  with  most  artificial  illuminants  (those 
based  on  incandescence)  reaches  a  maximum  still  further  in 
the  ultra-red  — and  a  specific  effect  depending  on  the  frequency. 

The  power  effect  is  general  and  probably  fairly  uniform 
throughout  the  exposed  tissue,  appears  simultaneous  with  or 
immediately  after  the  exposure,  and  thus  practically  no  danger 
of  harmful  results  from  destruction  of  tissue  exists,  as  excessive 
intensity  makes  itself  felt  immediately,  before  far-going  destruc- 
tion of  tissue  can  occur,  and,  therefore,  the  only  possible  danger 
which  could  exist  would  be  in  the  indirect  effect  of  stimulation 
on  other  organs  of  the  body,  as  the  heart.  Thus  the  use  of  in- 
candescent light  as  stimulant  appears  fairly  harmless. 

Different  is  the  specific  action  of  high-frequency  radiation. 
This  occurs  only  some  time  after  exposure,  from  a  few  hours  to 
several  weeks  (with  X-rays) .  As  these  higher  frequencies  are  not 
felt  by  the  body  as  such  and  exert  a  powerful  action  even  at  such 


58  RADIATION,  LIGHT,  AND  ILLUMINATION. 

low  intensities  that  their  energy  is  not  felt  as  heat,  and,  further- 
more, .  the  susceptibility  of  different  people  may  be  different, 
there  is  nothing  to  guard  against  excessive  and  thereby  harmful 
exposure.  Furthermore,  the  damage  is  far  more  severe  and 
lasting  than  with  the  power  effect,  and  fatal  cases  have  occurred 
years  after  exposure.  Possibly,  as  may  be  expected  from 
selective  action,  only  a  few  cells  in  the  living  tissue  are  killed 
by  the  radiation,  and  the  disintegration  products  of  these  dead 
cells  then  gradually  involve  the  surrounding  living  cells,  causing 
their  destruction  or  degeneration,  so  that  the  harm  is  far  out  of 
proportion  with  the  immediate  destructive  effect  of  the  radia- 
tion proper,  especially  with  penetrating  forms  of  radiation,  as 
X-rays  and  radium  rays,  in  which  the  lesions  are  correspondingly 
deep-seated. 

High-frequency  radiation  (violet,  ultra-violet,  X-ray)  should 
therefore  be  used  only  under  the  direction  of  experts  fully 
familiar  with  their  physiological  action  and  danger. 

The  specific  action  of  high-frequency  radiation  is  still  absent 
in  the  green,  begins  slightly  in  the  blue  and  violet,  increases 
into  the  ultra-violet  and  persists  up  to  the  highest  frequencies  of 
the  X-rays.  It  is  shared  also  by  the  radiation  of  the  radio-active 
substances,  as  the  alpha  and  beta  rays  of  radium.  While  the 
maximum  of  this  effect  probably  also  lies  in  the  ultra-violet, 
from  one  to  two  octaves  beyond  the  visible  spectrum,  the 
effect  is  profoundly  modified  by  the  transparency  or  opacity  of 
the  tissue  for  different  frequencies,  and  the  character  of  the  stimu- 
lating and  pathological  effects  greatly  depends  on  the  depth  to 
which  the  radiation  penetrates  the  body. 

The  largest  part  of  the  organism  is  water.  Water  is  trans- 
parent for  visible  light,  becomes  more  and  more  opaque  in  the 
ultra-red  as  well  as  in  the  ultra-violet,  and  is  again  fairly  trans- 
parent for  X-rays.  Blood  is  fairly  transparent  for  the  long 
visible  rays  of  red  and  yellow,  but  nearly  opaque  for  the  shorter 
violet  and  ultra-violet  rays.  Hence  next  to  the  X-rays  which 
can  pass  through  the  body,  the  longest  visible  rays  of  red  and 
yellow  penetrate  relatively  deepest  into  the  body,  though  even 
they  are  practically  absorbed  within  a  short  distance  from  the 
surface.  Thus  while  the  energy  maximum  of  the  sunlight 
is  in  the  ultra-red,  the  maximum  physiological  effect  probably 
is  that  of  the  red  and  yellow  rays :  the  same  which  are  the  active 


PHYSIOLOGICAL  EFFECTS  OF  RADIATION.  59 

rays  in  plant  life.  The  violet  and  ultra-violet  rays  are  absorbed 
close  to  the  surface  of  the  body  by  the  blood,  which  is  opaque 
for  them.  They  can  thus  be  made  to  penetrate  deeper  —  as  is 
done  in  their  therapeutic  use  —  by  freeing  the  tissue  of  the  body 
from  blood  by  compression  or  other  means.  Even  then,  how- 
ever, probably  only  the  longest  ultra-violet  rays  penetrate,  the 
very  short  ones  being  kept  out  by  the  opaque  character  of  the 
water  in  the  tissue. 

The  penetration  of  the  radiation  of  the  sunlight  into  the  human 
body  is  very  greatly  reduced  by  acclimatization,  which  leads 
to  the  formation  of  a  protective  layer  or  pigment,  more  or  less 
opaque  to  the  light.  Such  acclimatization  may  be  permanent 
or  temporary.  Permanent  acclimatization  has  been  evolved 
during  ages  by  those  races  which  developed  in  tropical  regions, 
as  the  negroes.  They  are  protected  by  a  black  pigment  under 
the  skin,  and  thereby  can  stand  intensities  of  solar  radiation 
which  would  be  fatal  to  white  men.  A  temporary  acclimatiza- 
tion results  from  intermittent  exposure  to  sunlight  for  gradually 
increasing  periods :  tanning,  and  enables  the  protected  to  stand 
without  harmful  effects  exposure  to  sunlight  which  would  pro- 
duce severe  sunburn  in  the  unprotected.  This  acquired  protec- 
tion mostly  wears  off  in  a  few  weeks,  but  some  traces  remain 
even  after  years. 

A  slight  protection  by  pigmentation  also  exists  in  white  men, 
and  its  differences  lead  to  the  observed  great  differences  in  sensi- 
tivity to  solar  radiation:  blondes,  who  usually  have  very  light 
pigmentation,  are  more  susceptible  to  sunburn  and  sunstroke  than 
the  more  highly  pigmented  brunette  people. 

In  sunburn  we  probably  have  two  separate  effects  super- 
imposed upon  the  other:  that  due  to  the  energy  of  the  solar 
radiation  and  the  specific  effect  of  the  high  frequencies,  which 
to  a  small  extent  are  contained  in  the  sunlight.  The  two  effects 
are  probably  somewhat  different,  and  the  high-frequency  effect 
tends  more  to  cause  inflammation  of  the  tissue,  while  the  energy 
effect  tends  towards  the  production  of  pigmentation  (tanning), 
and  the  symptoms  of  sunburn  thus  vary  with  the  different  pro- 
portions of  energy  radiation  and  of  high-frequency  radiation  as 
depending  on  altitude,  humidity  of  the  air,  the  season,  etc. 

30.  The  action  of  radiation  on  living  organisms  is  stimulating 
if  of  moderate  intensity,  destructive  if  of  high  intensity.  Thus 


60  RADIATION,  LIGHT,  AND  ILLUMINATION. 

it  is  analogous  with  that  of  any  other  powerful  agent  or  drug, 
as  alcohol,  caffeine,  etc.  The  intensity  of  light  which  is  destruc- 
tive to  life  largely  depends  on  the  amount  of  light  to  which  the 
organism  is  accustomed.  Those  organisms  which  live  in  the 
dark  may  be  killed  by  an  amount  of  light  which  is  necessary 
for  the  life  of  other  organisms.  Amongst  the  saprophytic  bacilli, 
for  instance  (the  germs  of  putrefaction),  many  species  live  in  the 
light,  and  die,  or  at  least  do  not  multiply,  if  brought  into  the 
dark,  while  other  putrefactive  bacilli  live  in  the  dark  and  are 
killed  by  light.  The  latter  also  is  the  case  with  the  pathogenic 
bacilli,  that  is,  the  disease  germs,  as  the  bacillus  of  tuberculosis, 
cholera,  etc.  As  these  live  in  the  dark,  the  interior  of  the  body, 
they  are  rapidly  killed  by  light.  Light,  and  radiation  in  general, 
therefore  is  one  of  the  most  powerful  germicides  and  disinfect- 
ants. One  of  the  most  effective  prophylactic  measures,  espe- 
cially against  the  diseases  of  civilization,  as  tuberculosis,  etc.,  thus 
is  to  flood  our  homes  with  light,  especially  direct  sunlight,  while 
our  habit  of  keeping  the  light  out  of  our  houses  by  curtains, 
shades,  etc.,  closing  our  residences  almost  light-tight,  when 
leaving  them  for  some  time,  converts  them  into  breeding  places 
of  disease  germs,  and  then  we  wonder  about  mortality. 

Obviously  excessive  light  intensity  ultimately  becomes  harm- 
ful even  to  the  human  organism,  and  it  is  therefore  advisable 
to  protect  ourselves  against  the  light  when  it  becomes  annoying 
by  its  intensity.  It  has  even  been  claimed  that  the  impossibility 
of  white  men  to  become  permanently  acclimatized  in  the  tropics 
and  the  change  in  the  temperament  of  the  population  of  our 
country  within  a  few  generations  from  their  immigration: 
the  increased  nervousness,  restlessness  and  "strenuousness," 
are  the  result  of  the  greater  intensity  of  the  sunlight,  especially 
its  high-frequency  radiation,  compared  with  the  more  cloudy 
climate  of  our  original  European  home.  Whether  this  is  the 
case  remains  to  be  further  investigated.  It  is  hard  to  believe, 
however,  that  such  a  profound  effect  should  result  from  the 
exposure  of  a  small  part  of  the  body,  face  and  hands,  to  a  more 
intense  light,  and  the  failure  of  acclimatization  in  the  tropics 
could  well  be  explained  by  the  higher  temperature  and  its  damag- 
ing effect,  while  the  change  from  Europe  to  America  is  not  merely 
a  change  from  a  more  cloudy  to  a  more  sunny  climate,  but 
from  a  maritime  climate,  that  is,  climate  having  fairly  uniform 


PHYSIOLOGICAL  EFFECTS  OF  RADIATION.  61 

and  slowly  changing  temperatures,  to  a  continental  climate, 
with  its  rapid  changes  of  temperature  and  enormous  temperature 
extremes,  and  the  difference  between  continental  and  maritime 
climate  may  be  suspected  as  the  cause  in  the  change  of  the  tem- 
perament of  the  races. 

As  men  have  lived  for  ages  in  the  light,  the  cells  of  the  human 
body  are  far  more  resisting  to  the  light  than  the  disease  germs, 
which  for  ages  have  lived  in  the  dark;  and  light,  and  more 
particularly  the  high-frequency  violet  and  ultra-violet  radiation 
and  the  X-rays,  thus  have  found  a  useful  therapeutic  application 
in  killing  disease  germs  in  the  human  body.  Thus,  by  expos- 
ing the  diseased  tissue  to  high-frequency  radiation,  the  disease 
germs  are  killed,  or  so  far  damaged  that  the  body  can  destroy 
them,  while  the  cells  of  the  body  are  still  unharmed,  but  stimu- 
lated to  greater  activity  in  combating  the  disease  germs.  As 
seen,  for  this  purpose  the  radiation  must  be  of  sufficient  intensity 
and  duration  to  kill  or  damage  the  bacilli,  but  not  so  intense 
as  to  harm  the  cells  of  the  body.  Surface  infections,  as  tubercu- 
losis of  the  skin  (scrofulosis,  lupus),  thus  are  effectively  and 
rapidly  cured  by  high-frequency  light.  More  difficult  and  less 
certain  the  effect  is  if  the  infection  is  deeper  seated,  as  then 
the  radiation  must  penetrate  a  greater  thickness  of  tissue  to 
reach  the  bacilli,  and  is  thereby  largely  absorbed,  and  the  danger 
thus  exists  that,  before  a  sufficient  intensity  of  radiation  can  be 
brought  to  the  seat  of  the  infection,  the  intensity  at  the  surface 
of  the  tissue  may  become  harmful  to  the  cells  of  the  body.  In 
this  case  the  more  penetrating  X-rays  would  be  more  applicable, 
as  they  can  penetrate  to  any  depth  into  the  body.  They  are, 
however,  so  far  distant  in  frequency  from  the  light  radiation, 
that  the  acclimatization  of  the  body  to  the  light  radiation 
probably  exists  only  to  a  lesser  extent  against  the  X-rays;  that 
is,  the  difference  in  the  destructive  effect  on  the  bacilli  and  on 
the  cells  of  the  body,  on  which  the  curative  effect  is  based,  prob- 
ably is  less  with  the  X-rays  than  with  the  long  ultra-violet  waves. 

Since  Dr.  Finsen  introduced  phototherapy  and  radiotherapy, 
about  fifteen  years  ago,  it  thus  has  found  a  very  extended  and 
useful  field,  within  its  limitation. 

This  greater  destructive  action  of  radiation  on  micro-organisms 
than  on  the  cells  of  the  human  body,  extends  not  merely  to  the 
pathogenic  bacilli,  but  to  all  organisms  living  in  the  dark. 


62  RADIATION,  LIGHT,  AND  ILLUMINATION. 

Thus  the  spermatozoa — which  biologically  are  independent 
living  organisms  — seem  to  be  killed  by  X-rays  before  any 
damage  is  done  to  the  body,  and  permanent  sterility  then 
results.  Amongst  the  cells  of  the  body  differences  seem  to  exist 
in  their  resistivity.  It  is  claimed,  for  instance,  that  the  sensory- 
nerves  are  first  paralyzed  by  violet  radiation  and  that  intense 
violet  light  can  thus  be  used  to  produce  local  anaesthesia,  suf- 
ficient for  minor  operations. 

Occasionally  the  effect  of  light  may  be  harmful  in  the  relation 
of  the  human  body  to  invading  bacilli.  In  some  eruptive  in- 
fections, as  smallpox,  ulceration  of  the  skin  (leading  to  mark- 
ing) seems  to  be  avoided  if  the  patient  is  kept  from  the  light, 
and  the  course  of  the  disease  mitigated.  As  red  light,  however, 
seems  to  have  no  effect,  instead  of  perfect  exclusion  of  light, 
which  is  not  very  feasible,  the  use  of  red  light  thus  seems  to  offer 
an  essential  advantage. 


LECTURE  IV. 
CHEMICAL    AND  PHYSICAL    EFFECTS   OF    RADIATION. 

Chemical  Effects. 

31.  Where  intense  radiation  is  intercepted  by  a  body  chemical 
action  may  result  by  the  heat  energy  into  which  the  radiation  is 
converted.  This,  however,  is  not  a  direct  chemical  effect  of 
radiation  but  an  indirect  effect,  resulting  from  the  energy  of  the 
radiation. 

Direct  chemical  effects  of  radiation  are  frequent.  It  is  such  an 
effect  on  which  photography  is  based :  the  dissociating  action  of 
radiation  on  silver  salts,  the  chloride  in  ordinary  photographic 
paper,  the  bromide  and  iodide  in  the  negative  plate  and  the  quick 
printing  papers.  This  chemical  action  is  greatest  in  the  violet 
and  ultra-violet  and  decreases  with  increasing  wave  length, 
hence  is  less  in  the  green,  small  in  the  yellow,  and  almost  absent  in 
the  red  and  ultra-red,  so  that  the  short  waves,  blue,  violet  and 
ultra-violet,  have  sometimes  been  called  "  chemical  rays."  This, 
however,  is  a  misnomer,  just  as  the  term  "heat  rays"  sometimes 
applied  to  red  and  ultra-red  rays.  In  so  far  as  when  intercepted 
they  are  converted  into  heat,  all  rays  are  heat  rays,  but  neither 
the  ultra-red  nor  any  other  radiation  is  heat,  but  it  may  become 
heat  when  it  ceases  to  be  radiation.  Thus  all  radiations  are 
chemical  rays,  that  is,  produce  chemical  action,  if  they  strike  a 
body  which  is  responsive  to  them. 

The  chemical  action  of  radiation  is  specific  to  its  frequency  and 
seems  to  be  some  kind  of  a  resonance  effect.  We  may  picture  to 
ourselves  that  the  frequency  of  vibration  of  a  silver  atom  is  that 
of  violet  or  ultra-violet  light,  and  therefore,  when  struck  by  a 
wave  of  this  frequency,  is  set  in  vibration  by  resonance,  just  as  a 
tuning  fork  is  set  in  vibration  by  a  sound  wave  of  the  frequency 
with  which  it  can  vibrate,  and  if  the  vibration  of  the  silver  atom, 
in  response  to  the  frequency  of  radiation,  becomes  sufficiently 
intense,  it  breaks  away  from  the  atom  with  which  it  is  chemically 


64  RADIATION,  LIGHT,  AND  ILLUMINATION. 

combined  in  the  compound,  the  silver  bromide,  etc.,  and  this 
compound  thus  splits  up,  dissociates.  The  phenomenon,  how- 
ever, must  be  more  complex,  as  a  simple  resonance  vibration 
would  be  especially  pronounced  at  one  definite  frequency,  the 
frequency  of  complete  resonance,  and  rapidly  decrease  for  higher 
and  for  lower  frequencies.  The  chemical  action  of  radiation  on 
silver  compounds,  however,  does  not  show  such  a  response  to  any 
definite  frequency,  but,  while  strongest  in  the  ultra-violet,  ex- 
tends over  the  entire  range  from  the  frequency  of  green  light 
beyond  the  ultra-violet  and  up  to  the  highest  frequencies  of 
X-rays.  That  the  chemical  activity  of  radiation  is  some  form  of 
resonance,  is,  however,  made  very  probable  by  the  relation  which 
exists  between  the  active  frequency  range  and  the  weight  of  the 
atom  or  molecule  which  responds  to  the  radiation.  Thus,  while 
the  fairly  heavy  silver  atom  (atomic  weight  108)  responds  to 
rays  near  the  violet  end  of  the  visible  spectrum,  the  much  lighter 
oxygen  atom  (atomic  weight  16)  responds  only  to  much  higher 
frequencies,  to  those  of  the  physiologically  most  destructive  rays, 
about  one  to  two  octaves  beyond  the  visible  spectrum.  These 
very  short  radiations  energetically  produce  ozone  03,from  oxygen 
02,  probably  by  dissociating  oxygen  molecules  02,into  free  atoms, 
and  these  free  atoms  then  join  existing  molecules:  0  +  02  =  03, 
thus  forming  ozone.  Possibly  their  destructive  physiological 
action  is  due  to  this  ability  to  cause  resonance  with  the  oxygen 
atom  and  thereby  destroy  molecular  structures. 

32.  Response  to  the  long  waves  of  red  and  ultra-red  light  thus 
may  be  expected  from  atoms  or  groups  of  atoms  which  are  very 
much  heavier  than  the  silver  atom,  and  this  indeed  seems  to  be 
the  case  in  the  action  of  radiation  on  the  life  of  the  plants.  There 
the  response  is  not  by  atoms,  but  by  the  much  heavier  groups  of 
atoms,  radicals  of  carbon  compounds,  which  separate  and  recom- 
bine  in  response  to  radiations  and  thus  produce  in  vegetable 
organisms  the  metabolism  which  we  call  life. 

The  action  of  radiation  on  plant  life  thus  seems  to  be  a  chemi- 
cal action,  and  this  would  be  the  most  important  chemical  action, 
as  on  it  depends  the  life  of  the  vegetation  and  thereby  also  the 
existence  of  animal  life  and,  thus,  our  own.  This  action  by  which 
the  vegetation  converts  the  energy  of  radiation  into  chemical 
energy  is  related  to  the  presence  of  chlorophyl,  a  green  body 
which  exhibits  a  red  fluorescence.  I  show  you  here  a  solution 


CHEMICAL  AND  PHYSICAL  EFFECTS  OF  RADIATION.     65 

thereof  in  alcohol.  This  use  of  the  energy  of  radiation  occurs 
only  in  those  parts  of  the  plant  in  which  chlorophyl  is  present, 
usually  shown  by  its  green  color,  that  is,  in  the  leaves  and  young 
stems.  In  those  plants  in  which  the  leaves  have  lost  their  chloro- 
phyl in  taking  up  other  functions  —  as  the  function  of  protection 
against  attack  by  conversion  into  spines  in  the  cacti  —  the  stems 
and  trunks  have  acquired  the  function  of  energy  supply  from 
radiation,  and  show  the  green  color  of  chlorophyl.  When  the 
leaves  die  in  the  fall  their  chlorophyl  disappears  and  they  change 
to  yellow  or  red  color.  Those  parts  of  the  plants  which  contain 
chlorophyl,  mainly  the  leaves,  take  carbon  dioxide  (C02)  from 
the  air  through  breathing  openings  (stomata),  absorb  the  radia- 
tion, and  convert  its  energy  into  chemical  energy,  and  use  this 
energy  in  splitting  up  or  dissociating  the  C02,  exhausting  the 
oxygen  02  and  using  the  carbon  in  producing  the  complex  carbon 
compounds  of  their  structure:  fiber  (cellulose),  starch,  proto- 
plasm, etc.  The  energy  of  plant  life  thus  is  derived  from  radia- 
tion and  their  work  is  constructive  or  synthetic,  that  is,  they 
produce  complex  chemical  compounds  from  simple  ones:  the 
carbon  dioxide  of  the  air,  the  nitrates  and  phosphates  of  the  soil, 
etc.  Inversely,  the  animal  organism  is  analytic,  it  converts  the 
chemical  energy  of  complex  compounds  into  mechanical  and 
heat  energy  by  splitting  them  into  simpler  compounds,  burning 
them  in  the  lungs  or  gills.  For  the  supply  of  mechanical  energy 
which  maintains  the  life,  the  animal  organism  thus  depends  upon 
the  synthetic  work  of  the  vegetation  by  consuming  as  food  the 
complex  compounds  constructed  by  the  plants  from  the  energy 
of  radiation,  either  directly  (vegetarians),  or  indirectly,  by  eating 
other  animals,  which  in  their  turn  live  on  the  vegetation.  Thus, 
while  the  plants  take  in  from  the  air  carbon  dioxide  C02,  exhaust 
the  oxygen  02,  and  convert  the  C  into  complex  compounds,  the 
animal  takes  in  oxygen  02,  by  it  burns  up  the  complex  carbon 
compounds  derived  from  the  plants,  and  exhausts  C02  as  product 
of  combustion,  but  in  its  ultimate  result,  all  life  on  the  earth  de- 
pends for  its  energy  on  radiation,  which  is  made  available  in  the 
plants  by  conversion  to  chemical  energy  and  used  as  such  by  the 
animals. 

The  radiations  which  supply  the  energy  of  plant  life,  probably 
are  the  long  waves  of  yellow,  red  and  ultra-red  light,  while  the 
short  waves  of  blue,  violet  and  ultra-violet  cannot  be  used  by  the 


66  RADIATION,  LIGHT,  AND  ILLUMINATION. 

plant,  but  are  harmful,  kill  the  vegetation.  This  can  easily  be 
understood :  to  the  long  waves  of  red  and  yellow  light  the  atoms 
do  not  respond,  but  only  the  much  heavier  groups  of  atoms  or  car- 
bon radicals,  and  these  thus  separate  and  recombine  and  thereby 
constitute  what  we  call  life.  To  very  short  waves,  that  is,  high 
frequencies,  these  heavy  groups  of  atoms  cannot  respond,  but 
single  atoms  would  respond  thereto  and  thus  by  their  separation 
break  up  and  destroy  the  atomic  groups.  That  is,  the  resonant 
dissociation  produced  by  low  frequency  of  radiation  extends  only 
to  the  groups  of  atoms  and  thereby  results  in  their  separation  and 
recombination  to  heavier  molecules :  life,  while  the  resonant  dis- 
sociation produced  by  high  frequencies  extends  to  the  atom  and 
thereby  splits  up  and  destroys  the  molecules  of  the  living  organ- 
ism, that  is,  death.  Therefore  the  short  waves  of  radiation, 
green,  blue,  etc.,  which  are  more  or  less  harmful  to  plants,  are 
not  used  but  are  reflected  by  the  chlorophyl;  hence  the  green 
color.  To  some  extent  violet  radiation  is  absorbed  by  chloro- 
phyl, but  it  is  questionable  whether  the  energy  of  violet  light 
directly  contributes  to  the  chemical  action,  and  it  is  rather 
probable  that  the  violet  radiation  is  converted  into  red  light  by 
fluorescence  —  chlorophyl  fluoresces  red  —  and  used  as  red 
light.  Excessive  violet  radiation  seems  to  be  harmful. 

Physical  Effects. 

33.  Some  of  the  most  interesting  physical  effects  of  radiation 
are  those  by  which  it  is  converted  into  another  form  of  radiation : 
fluorescence  and  phosphorescence. 

Many  substances  have  the  property  of  converting  some  of  the 
radiation  which  is  absorbed  by  them  into  radiation  of  a  different 
wave  length,  that  is,  act  as  frequency  converter  of  radiation, 
fluorescence.  Many  bodies  when  exposed  to  radiation  store  some 
of  the  energy  of  radiation  in  such  a  manner  as  to  give  it  out  again 
afterwards  and  thus,  after  exposure  to  light,  glow  in  the  darkness 
with  gradually  decreasing  intensity,  phosphorescence.  These 
phenomena  probably  belong  to  the  least  understood  effects 
of  radiation.  They  are  very  common,  but  phosphorescence 
usually  lasts  such  a  short  time  that  it  can  be  observed  only 
by  special  apparatus,  although  a  few  bodies  continue  to  phos- 
phoresce for  hours  and  even  days.  Fluorescence  also  is  usually 


CHEMICAL  AND  PHYSICAL  EFFECTS  OF  RADIATION.     67 

so  weak  as  to  escape  notice,  although  in  a  few  bodies  it  is  very 
strong. 

The  change  of  frequency  in  fluorescence  always  seems  to  be  a 
lowering  of  the  frequency,  that  is,  an  increase  of  wave  length,  and 
in  phosphorescence  also  the  light  given  out  seems  always  to  be 
of  lower  frequency  than  the  light  absorbed  and  indeed,  fluores- 
cence and  phosphorescence  seem  to  be  essentially  the  same 
phenomenon,  radiation  is  absorbed  and  its  energy  given  out  again 
as  radiation  of  lower  frequency  and  that  part  of  the  returned 
radiation  which  appears  during  the  absorption  we  call  fluores- 
cence, that  part  which  appears  later,  phosphorescence.  There  is, 
however,  frequently  a  change  of  the  color  of  the  light  between 
fluorescence  and  phosphorescence  and  also  between  phosphores- 
cence immediately  after  exposure  to  light  and  some  time  after- 
wards. For  instance,  some  calcite  (calcium  carbonate  or  lime- 
stone) fluoresces  crimson,  but  phosphoresces  dark  red.  The 
phosphorescence  of  calcium  sulphide  changes  from  blue  in  the 
beginning  to  nearly  white  some  time  after,  etc. 

Due  to  the  change  of  frequency  to  longer  waves  the  longest 
visible  rays,  red,  orange  and  yellow,  produce  no  fluorescence  or 
very  little  thereof,  as  their  fluorescent  and  phosphorescent  radia- 
tion would  usually  be  beyond  the  red,  in  the  invisible  ultra-red. 
Blue,  violet  and  ultra-violet  light  produce  the  most  intense 
effects,  as  a  lowering  in  frequency  of  these  radiations  brings  them 
well  within  the  visible  range. 

Ultra-violet  light  is  best  suited  for  studying  fluorescence  as  it  is 
not  visible,  and  thus  only  the  fluorescent  light  is  visible;  white 
light,  for  instance,  does  not  show  the  same  marked  effect,  since  the 
direct  white  light  is  superimposed  upon  the  light  of  fluorescence. 
Most  brilliant  effects,  however,  are  produced  by  using  a  source  of 
light  which  is  deficient  in  the  frequencies  given  by  fluorescence 
and  then  looking  at  the  fluorescent  body  through  a  glass  having 
the  same  color  as  that  given  by  fluorescence.  Thus  the  least 
traces  of  red  fluorescence  can  be  discovered  by  looking  at  the 
body  through  a  red  glass,  in  the  illumination  given  by  the  mer- 
cury lamp.  As  the  mercury  lamp  contains  practically  no  red 
rays,  seen  through  a  red  glass  everything  appears  nearly  black  or 
invisible  except  red  fluorescent  bodies,  which  appear  self-lumi- 
nous, glowing  in  a  light  of  their  own,  and  appear  like  red  hot 
bodies. 


68  RADIATION,  LIGHT,  AND  ILLUMINATION. 

In  the  illumination  given  by  the  mercury  lamp  I  here  drop  a 
few  drops  of  a  solution  of  rhodamine  6  G,  rhodamine  R  and 
uranine  (aniline  dyes)  into  a  large  beaker  of  water.  As  you  see, 
when  sinking  down  and  gradually  spreading,  they  appear  — 
especially  against  a  dark  background  —  as  brilliant  luminous 
clouds  of  orange,  red  and  green,  and  seen  through  a  red  glass 
they  appear  like  clouds  of  fire.  I  change  to  the  illumination 
given  by  the  incandescent  lamp  and  all  the  brilliancy  disappears, 
fluorescence  ceases  and  we  have  a  dull  red  colored  solution.  I 
show  you  here  the  sample  card  of  a  silk  store  of  different  colored 
silks.  Looking  at  it  through  a  red  glass,  in  the  mercury  light  all 
disappear  except  a  few,  which  you  can  pick  out  by  their  lumi- 
nosity: they  are  different  colors,  pinks,  reds,  heliotrope,  etc.,  but 
all  containing  the  same  red  fluorescent  aniline  dye,  rhodamine. 
A  glass  plate  coated  with  a  thick  layer  of  transparent  varnish, 
colored  by  rhodamine,  appears  like  a  sheet  of  red  hot  iron  in  the 
mercury  light,  especially  through  a  red  glass,  while  in  the  light  of 
the  incandescent  lamp  it  loses  all  its  brilliancy. 

This  solution  of  rhodamine  6  G  in  alcohol,  fluoresces  a  glaring 
orange  in  the  mercury  light,  in  the  light  of  a  carbon  arc  lamp  (or 
in  daylight)  it  fluoresces  green  and  less  brilliant.  Thus  you  see 
that  the  color  of  the  fluorescent  light  is  not  always  the  same,  but 
depends  to  some  extent  on  the  frequency  of  radiation  which 
causes  the  fluorescence. 

Here  I  have  a  sheet  of  paper  covered  with  calcium  sulphide 
and  a  lump  of  willemite  (zinc  silicate)  and  some  pieces  of  calcite. 
As  you  see,  none  of  them  show  any  appreciable  fluorescence 
in  the  mercury  light.  But  if  I  turn  off  the  mercury  light,  the 
calcium  sulphide  phosphoresces  brightly  in  a  blue  glow,  the  others 
do  not.  Now  I  show  you  all  three  under  the  ultra-violet  rays  of 
the  condenser  discharge  between  iron  terminals,  or  ultra-violet 
lamp  (Fig.  11)  and  you  see  all  three  fluoresce  brilliantly,  in  blue, 
green  and  red.  Turning  off  the  light  all  three  continue  to  glow 
with  about  the  same  color,  that  is,  phosphoresce,  but  the  red 
fluorescence  of  the  calcite  very  rapidly  decreases,  the  green  glow 
of  the  willemite  a  little  slower,  but  the  blue  glow  of  the  calcium 
sulphide  screen  persists,  decreasing  very  little.  I  now  hold  my 
hand  back  of  it  and  close  to  it  and  you  see  the  picture  of  the  hand 
appear  on  the  screen  by  an  increase  of  the  luminosity  where  by 
contact  with  the  hand  the  temperature  of  the  screen  was  slightly 


CHEMICAL  AND  PHYSICAL  EFFECTS  OF  RADIATION.      69 

raised,  thus  showing  the  effect  of  the  temperature  rise  in  increas- 
ing phosphorescence. 

These  substances  which  I  show  you,  calcium  sulphide,  cal- 
cium carbonate  (calcite),  zinc  silicate  (willemite),  are  not  fluo- 
rescent or  phosphorescent  themselves,  but  their  luminescence  is 
due  to  a  small  percentage  of  some  impurities  contained  in  them. 
Chemically  pure  substances  and  concentrated  solutions  of  the 
aniline  dyes,  or  these  dyes  in  their  solid  form,  do  not  show  the 
luminescence,  but  only  when  in  very  diluted  solutions;  that  is, 
luminescence  as  fluorescence  and  phosphorescence  seems  to  be 
the  property  of  very  diluted  solutions  of  some  substances  in 
others.  Thus  a  sheet  of  paper  or  cardboard  colored  red  by 
rhodamine  does  not  fluoresce,  but  if  a  small  quantity  of  rhoda- 
mine  is  added  to  some  transparent  varnish  and  the  paper  colored 
red  by  a  heavy  layer  of  this  varnish  it  fluoresces  brightly  red. 

To  show  you  the  fluorescent  spectrum,  I  have  here  a  mercury 
lamp  surrounded  by  a  very  diluted  solution  of  rhodamine  6  G, 
and  some  rhodamine  R,  contained  between  two  concentric  glass 
cylinders.  As  you  see,  through  the  spectroscope  a  broad  band 
appears  in  the  red  and  the  green  light  has  faded  considerably. 
You  also  notice  that  the  light  of  this  lamp,  while  still  different 
from  white  light,  does  not  give  anything  like  the  ghastly  effect  of 
human  faces,  as  the  plain  mercury  lamp,  but  contains  considerable 
red  rays,  though  not  yet  enough.  I  also  show  you  a  mercury 
lamp  surrounded  by  a  screen  of  a  very  dilute  solution  of  uranine: 
you  see,  its  light  is  bright  greenish  yellow,  but  much  less  ghastly 
than  the  plain  mercury  light  and  the  spectroscope  shows  the 
mercury  lines  on  a  fluorescent  spectrum,  which  extends  as  a  con- 
tinuous luminous  band  from  the  green  to  and  beyond  the  red. 
You  also  see  that  with  this  uranine  screen  the  mercury  lamp 
gives  more  light  than  without  it :  considerable  of  its  ultra-violet 
and  violet  light  is  converted  to  yellow  and  thereby  made  visible 
or  more  effective. 


LECTURE   V. 
TEMPERATURE    RADIATION. 

34.  The  most  common  method  of  producing  radiation  is  by 
impressing  heat  energy  upon  a  body  and  thereby  raising  its  tem- 
perature. Up  to  a  short  time  ago  this  was  the  only  method  avail- 
able for  the  production  of  artificial  light.  The  temperature  is 
raised  by  heating  a  body  by  the  transformation  of  chemical 
energy,  that  is,  by  combustion,  and  in  later  years  by  the  trans- 
formation of  electric  energy,  as  in  the  arc  and  incandescent 
lamp. 

With  increasing  temperature  of  a  body  the  radiation  from  the 
body  increases.  Thus,  also,  the  power  which  is  required  to  main- 
tain the  body  at  constant  temperature  increases  with  increase  of 
temperature.  In  a  vacuum  (as  approximately  in  the  incandes- 
cent lamp) ,  where  heat  conduction  and  heat  convection  from  the 
radiating  body  is  excluded,  all  the  power  input  into  the  body  is 
radiated  from  it,  and  in  this  case  the  power  input  measures  the 
power  of  the  radiation. 

The  total  power  or  rate  at  which  energy  is  radiated  by  a  heated 
body  varies  with  the  fourth  power  of  its  absolute  temperature, 
that  is : 

If  A  =  surface  area,  Tl  =  absolute  temperature  of  the  radia- 
tor and  T2  =  absolute  temperature  of  the  surrounding  objects 
on  which  the  radiation  impinges :  the  total  power  radiated  by  the 
body  is  (Stefan's  Law) : 

Pr  =  kA  (TV  -  ?V),  (1) 

where  for  a  black  body,  as  the  carbon  filament  with  Pr  given 
in  watts  per  square  cm.  k  is  of  the  magnitude 

k  =  5  X  1(T12;  (2) 

!T2  is  usually  atmospheric  temperature  or  about  300  degrees  abs. 

If  Tl  does  not  differ  much  from  Tv  that  is,  when  considering 

the  radiation  of  a  body  raised  slightly  above  the  surround- 

70 


TEMPERATURE  RADIATION.  71 

ing  temperature,  as  an  electric  machine,  equation  (1)  can  be 
written : 

Pr  =  kA  (T,  -  T2)  (TV  +  T*T2  +  7\7y  +  7y); 
or,  approximately, 

Pr  =  4  kAT*  (T,  -  T),  (3) 

where  T  is  the  room  temperature  (Tl  —  T)  the  temperature  rise 
of  the  radiator  above  room  temperature;  that  is,  for  moderate 
temperature  differences  the  radiation  power  is  proportional  to 
the  temperature  rise. 

This  equation  (3)  gives  the  law  generally  used  for  calculating 
temperature  rise  in  electric  machinery  and  other  cases  where  the 
temperature  rise  is  moderate.  Obviously,  in  air  the  power  given 
off  by  the  heated  body,  P,  is  greater  than  the  power  radiated,  Pr, 
due  to  heat  convection  by  air  currents,  etc.,  but  as  heat  conduc- 
tion and  convection  also  are  approximately  proportional  to  the 
temperature  rise,  as  long  as  the  latter  is  moderate,  equation  (3) 
can  still  be  used,  but  with  the  numerical  value  of  k  increased  to 
k^  so  as  to  include  the  heat  conduction  and  convection:  in 
stationary  air  A^  reaches  values  as  high  as  fct  =  25  X  10~12  to 
50  X  10~12. 

As  soon,  however,  as  the  temperature  rise  (Tl  —  T)  becomes 
comparable  with  the  absolute  temperature  T,  the  equation  (3) 
can  no  longer  be  used,  but  the  complete  equation  (1)  must  be 
used,  and  when  the  temperature  of  the  radiator,  Tv  is  very  much 
greater  than  the  surrounding  temperature  T2,  T24  becomes  negli- 
gible compared  with  7\4  and  equation  (1)  can,  for  high  tempera- 
tures, thus  be  approximated  by: 

Pr  =  kATf;  (4) 

That  is,  the  radiation  power,  as  function  of  the  temperature, 
gradually  changes  from  proportionality  with  the  temperature 
rise,  at  low  temperature  rise,  to  proportionality  with  the  fourth 
power  of  the  temperature  for  high  temperature  rises. 

Inversely  then,  with  increasing  power  input  into  the  radiator 
and  thus  increasing  radiation  power,  its  temperature  first  rises 
proportional  to  the  power  input  and  then  slower  and  ultimately 
approaches  proportionality  with  the  fourth  root  of  the  power 
output:  4/p- 

T  =V  — • 
ll      V  kA 


72 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


In  Fig.  27  is  shown  the  radiation  curve,  with  the  temperatures 
T  as  ordinates  and  the  radiated  power  Pr  as  abscissas,  the  upper 
curve  with  100  times  the  scale  of  abscissas. 

Thus,  to  double  the  temperature  rise  from  10  deg.  cent,  to  20 
deg.  cent,  requires  doubling  the  power  input.  To  double,  how- 
ever, the  temperature  rise  from  1000  deg.  cent,  to  2000  deg.  cent, 
requires  an  increase  of  the  power  input  from  12734  to  22734,  or 
more  than  ten  fold.  At  high  temperature  the  power  input,  there- 
fore, increase  enormously  with  the  increase  of  temperature. 


FIG.  27. 

With  bodies  in  a  vacuum,  the  radiation  power  is  the  power 
input  and  this  above  law  can  be  used  to  calculate  the  tempera- 
ture of  the  radiator  from  the  power  input.  In  air,  however,  a 
large  part  of  the  energy  is  carried  away  by  air  currents,  and 
this  part  of  the  power  does  not  strictly  follow  the  temperature 
law  of  radiation,  equation  (1).  For  radiators  in  stationary  air 
(that  is,  not  exposed  to  a  forced  blast,  as  the  centrifugal  blast  of 
revolving  machinery),  the  total  power  input  for  high  tempera- 
ture (as  expended  by  radiation  and  heat  convection)  varies  with 
a  high  power  of  the  temperature,  so  that  the  radiation  law  equa- 
tion (1)  can  still  be  used  to  get  a  rough  approximation  of  the 
relative  values  of  temperatures. 

It,  therefore,  is  not  permissible  to  assume  the  temperature  rise 
as  proportional  to  the  power  input  as  soon  as  the  temperature 


TEMPERATURE  RADIATION.  73 

rise  is  considerable  and  even  in  electrical  apparatus  of  fire-proof 
construction  as  some  rheostats,  etc.,  where  a  higher  temperature 
rise  is  permitted,  the  calculation  of  this  temperature  rise  must  be 
approximated  by  the  general  law  (1)  and  not  the  law  of  propor- 
tionality (3),  as  the  latter  would  'give  entirely  wrong  results. 
For  instance,  assuming  a  temperature  rise  of  50  deg.  cent,  per 
watt  per  sq.  in.  a  cast  silicon  rod,  which  —  at  bright  incandes- 
cence —  can  dissipate  200  watts  per  sq.  in.  would  give  by  (3),  a 
temperature  rise  of  10,000  deg.  cent.  This  obviously  is  impos- 
sible, as  silicon  melts  at  about  1400  deg.  cent. 

35.  With  increasing  temperature  of  the  radiator,  the  intensity 
of  the  radiation  increases,  and  at  the  same  time  the  average 
frequency  of  radiation  also  increases,  that  is,  the  higher  frequen- 
cies increase  more  rapidly  than  the  lower  frequencies  and  higher 
and  higher  frequencies  appear,  until  ultimately  frequencies  are 
reached  where  the  radiation  becomes  visible  to  the  eye,  as  light. 
When  with  increasing  temperature  the  radiation  just  begins  to  be 
visible,  it  appears  as  a  faint  colorless  grey,  "gespenster  grau" 
exhibiting  the  same  weird  and  indistinct  appearance  as  are  seen 
at  higher  intensities  in  the  monochrome  blue  and  violet  radia- 
tions ;  that  is,  we  see  a  faint  grey  light,  but  when  we  look  at  it,  it 
has  disappeared :  the  reason  is  that  the  sensitivity  of  the  sensitive 
spot  of  the  eye  for  very  faint  light  is  less  than  that  of  the  surround- 
ing retina  and  the  first  glimmer  of  light  thus  disappears  as  soon 
as  we  focus  it  on  the  sensitive  spot.  With  increasing  tempera- 
ture, first  the  lowest  of  the  visible  frequencies  appear  and  become 
visible  as  red  light,  and  with  still  further  increase  of  temperature 
gradually  orange,  yellow,  green,  blue,  violet  and  ultra-violet  rays 
appear  and  the  color  thus  changes  from  red  to  orange,  yellow, 
yellowish  white  and  then  white,  the  latter  at  that  temperature 
where  all  the  visible  radiations  are  present  in  the  same  propor- 
tion as  in  daylight.  With  still  further  increase  of  temperature, 
the  violet  end  of  the  spectrum  would  increase  faster  than  the  red 
end  and  the  light  thus  shift  to  bluish  white,  blue  and  violet. 

The  invisibility  of  the  radiation  of  low  temperature  is  not  due 
to  low  intensity.  I  have  here  an  incandescent  lamp  at  normal 
brilliancy.  If  I  decrease  the  power  input  and  thereby  the  radi- 
ated power  to  T^  it  becomes  invisible,  but  if  we  move  away  from 
the  lamp  to  10  times  the  previous  distance,  we  get  only  T^  the 
radiation  reaching  our  eyes  and  still  the  light  is  very  plainly 


74  RADIATION,  LIGHT,  AND  ILLUMINATION. 

visible.    The  invisibility  in  the  former  case,  thus,  is  not  due  to  low 
intensity,  but  to  low  frequency. 

The  fraction  of  the  total  radiation,  which  is  visible  to  the  eye 
as  light,  thus  increases  with  the  increasing  temperature,  from 
zero  at  low  temperature  —  where  the  radiator  does  not  give 
sufficiently  high  frequencies  to  be  visible  —  and  very  low  values 
when  it  just  begins  to  be  visible  in  red  light,  to  a  maximum  at  that 
temperature  where  the  average  frequency  of  the  radiation  is  in 
the  visible  range,  and  it  would  decrease  again  for  still  higher 
temperature  by  the  average  frequency  of  radiation  shifting 
beyond  the  visible  into  the  ultra-violet.  The  efficiency  of  light 
production  by  incandescence  thus  rises  with  increasing  tempera- 
ture to  a  maximum,  and  then  decreases  again.  As  the  total 
radiation  varies  with  the  fourth  power  of  the  temperature,  it  thus 
follows  that  the  visible  radiation  first  varies  with  a  higher  power 
of  the  temperature  than  the  fourth,  up  to  the  maximum  efficiency 
point,  and  beyond  that  increases  with  less  than  the  fourth  power 
of  the  temperature.  The  temperature  at  which  the  maximum 
efficiency  of  light  production  by  incandescence  occurs,  that  is, 
where  the  average  frequency  of  temperature  radiation  is  in  the 
visible  range,  probably  is  between  5000  and  8000  deg.  cent,  and 
as  the  most  refractory  body,  carbon,  boils  at  3750  deg.  cent.,  this 
temperature  thus  is  unattainable  with  any  solid  or  liquid  radiator. 

Practically  all  bodies  give  the  same  temperature  radiation, 
that  is,  follow  the  temperature  law  (1),  differing  only  by  the 
numerical  value  of  the  constant  fc;  that  is,  with  increase  of 
temperature  the  radiation  intensity  increases  and  the  average 
frequency  of  radiation  increases  in  the  same  manner  with  most 
solid  and  liquid  bodies,  so  that  at  the  same  temperature  all  the 
bodies  of  normal  temperature  radiation  give  the  same  radiation 
curve;  that  is,  the  same  distribution  of  intensity  as  function  of 
the  frequency  and  thus  the  same  fraction  of  visible  to  total  radia- 
tion, that  is,  the  same  efficiency  of  light  production. 

If  T  is  the  absolute  temperature  in  deg.  cent,  and  lw  the  wave 
length  of  radiation,  the  power  radiated  at  wave  length  /„,  and 
temperature  T1  by  normal  temperature  radiation  is : 

b 
P  (IJ  =  c,Alw  %     ^ ,     (Wien's  law) ; 

or'  r  •  i.  *      r1 

P  (U  =  c,Alw  a\e     V-l\          (Planck's  law) ; 


TEMPERATURE  RADIATION.  75 

where  a  =  5  for  normal  temperature  radiation  or  black  body 
radiation;  b  =  1.42,  and  A  =  surface  area  of  the  radiator. 

Integrating  the  formula  of  Wien's  law  over  lw  from  0  to  oo , 
gives  the  total  radiation : 


P-    f  °°P  (lw)dlw  =  Mr-1; 
«/o 

thus,  for  a  =  5; 


or,  Stephan's  law,  as  discussed  above. 

The  maximum  energy  rate  at  temperature  T  occurs  at  the  wave 
length  lw  =  lm  given  by: 

dP  (lw) 

~Ji —  =  °> 

dlw 

which  gives: 

lmT  =-  =  0.284; 
a 

or, 

0.284 


=  50  X  10~6     thus  gives: 
T  -  =  5680  deg. 


With  normal  temperature  radiation  the  efficiency  of  light  pro- 
duction is  thus  merely  a  function  of  the  temperature  and  does 
not  depend  upon  the  material  of  the  radiating  body,  provided 
that  the  material  is  such  as  to  withstand  the  temperature. 

As  the  efficiency  maximum  of  normal  temperature  radiation  is 
far  beyond  the  attainable,  within  the  range  of  temperature  avail- 
able up  to  the  boiling  point  of  carbon,  the  efficiency  of  light  pro- 
duction by  incandescence  continuously  increases,  but  even  then 
the  octave  of  visible  radiation  is  at  the  far  upper  end  of  the  radia- 
tion curve,  and  thus  the  problem  of  efficient  light  production  is 
to  operate  the  radiator  at  the  highest  possible  temperature. 

The  efficiency  of  light  production  is  rather  low  even  at  the 
maximum  efficiency  point  and  with  the  average  frequency  of 
radiation  in  the  visible  range,  since  this  visible  range  is  less  than 
one  octave;  under  these  most  favorable  conditions  the  visible 


76  RADIATION,  LIGHT,  AND  ILLUMINATION. 

energy  probably  does  not  much  exceed  20  per  cent  of  the  total 
radiation,  the  rest  falls  below  and  above  the  visible  frequencies. 

36.  At  the  highest  attainable  temperature,  the  boiling  point 
of  carbon,  the  efficiency  is  much  lower,  probably  below  10  per 
cent  and  this  would  be  the  highest  efficiency  attainable  by  normal 
temperature  radiation.  It  is  utilized  for  light  production  in  the 
carbon  arc  lamp.  The  carbon  arc  flame  gives  practically  no 
light,  but  all  the  light  comes  from  the  incandescent  tips  of  the 
carbon  electrodes,  mainly  the  positive,  which  are  at  the  boiling 
point  of  carbon  and  thus  give  the  most  efficient  temperature 
radiation. 

Obviously,  in  the  carbon  arc  lamp  a  very  large  part  of  the 
energy  is  wasted  by  heat  conduction  through  the  carbons,  heat 
convection  by  air  currents,  etc.,  and  the  total  efficiency  of  the 
carbon  arc  lamp,  that  is,  the  ratio  of  the  power  of  the  visible 
radiation  to  the  total  electric  power  input  into  the  lamp,  thus  is 
much  lower  than  the  radiation  efficiency,  that  is,  the  ratio  of  the 
power  of  the  visible  to  the  total  radiation. 

Thus  the  efficiency  of  the  carbon  arc  is  considerably  increased 
by  reducing  the  loss  by  heat  conduction,  by  the  use  of  smaller 
carbons  —  the  life  of  the  carbons,  however,  is  greatly  reduced 
thereby,  due  to  their  more  rapid  combustion. 

The  carbon  arc  lamp  thus  gives  the  most  efficient  incandescent 
light,  as  it  operates  at  the  highest  temperature,  the  boiling  point 
of  carbon.  But  by  doing  so  the  radiator  is  continuously  con- 
sumed and  has  to  be  fed  into  the  arc.  This  requires  an  operating 
mechanism  and  becomes  feasible  only  with  large  units  of  light. 

To  attain  the  highest  possible  efficiency  of  light  production  by 
temperature  radiation  with  a  permanent  radiator,  thus  requires 
the  use  of  extremely  refractory  bodies,  since  the  efficiency  in- 
creases with  the  increase  of  the  temperature,  and  is  still  very 
low  at  the  melting  point  of  platinum. 

To  exclude  all  the  losses  of  energy  by  heat  conduction  and 
heat  convection,  the  radiator  is  enclosed  in  a  vacuum,  so  that  all 
the  power  input  is  converted  into  radiation.  Even  in  this  case 
the  efficiency  of  light  production  is  still  relatively  low. 

The  vacuum  used  in  the  incandescent  lamp,  thus,  is  not  only 
for  the  purpose  of  protecting  the  filament  from  combustion. 
Filling  the  globe  with  some  gas  which  does  not  attack  the  carbon 
would  do  this  and  yet  it  would  very  greatly  lower  the  efficiency, 


TEMPERATURE  RADIATION. 


77 


as  can  be  seen  by  admitting  air  into  the  lamp  bulb,  when  the 
filament  drops  down  to  dull  red  heat,  before  it  burns  through. 
With  a  metal  filament  lamp  this  can  be  seen  still  plainer,  as  the 
filament  lasts  longer  in  air. 

A  search,  thus,  has  been  made  and  is  still  being  made,  through- 
out the  entire  range  of  existing  bodies,  for  very  refractory  mate- 
rials. Such  materials  may  be  chemical  elements  or  compounds. 
However,  the  combination  of  a  refractory  element  with  one  of 
very  much  lower  melting  point  lowers  its  melting  point,  and  very 
refractory  compounds,  thus,  may  be  expected  only  amongst  the 
combinations  of  very  refractory  elements  with  each  other. 

The  chemical  elements,  arranged  in  order  of  their  atomic 
weight,  exhibit  a  periodicity  in  their  properties  which  permits 


FIG.  28. 


a  systematic  study  of  their  properties.  In  diagram  Fig.  28  the 
elements  are  arranged  in  order  of  their  atomic  weight  in  the 
"periodic  system." 

The  height  of  their  melting  point  is  indicated  by  the  darkness 
of  the  background.  That  is,  the  most  refractory  elements, 
wolfram  and  carbon,  are  shown  on  black  background.  The  ele- 
ments of  somewhat  lower,  but  still  so  very  high  melting  point 
that  they  cannot  be  fused  by  any  temperature  attainable  by 
combustion,  but  require  the  electric  furnace,  are  shown  on  cross 
shaded  background.  Inversely,  the  elements  of  the  lowest  melt- 
ing point,  mercury  under  the  metals  and  helium  under  metal- 


78  RADIATION,  LIGHT,  AND  ILLUMINATION. 

loids,  are  shown  on  white  background,  and  the  easily  fusible 
metals  and  gaseous  metalloids  on  lightly  shaded  background. 

As  seen,  there  are  two  peaks  of  refractoriness,  one  amongst  the 
metalloids,  in  carbon,  and  one  under  the  metals  in  wolfram  (or 
tungsten),  and  around  these  two  peaks  all  the  refractory  elements 
are  grouped.  Inversely,  there  are  also  two  depressions,  or  points 
of  minimum  melting  point,  in  helium  under  the  metalloids, 
around  which  all  the  gaseous  elements  are  grouped,  and  in  mer- 
cury under  the  metals,  around  which  all  the  easily  fusible  metals 
are  grouped. 

It  is  interesting  to  note  that  the  melting  point  rises  towards 
wolfram  from  both  sides,  as  diagrammatically  illustrated  at  the 
top  of  Fig.  28,  in  such  a  manner  that  the  maximum  point 
should  be  expected  in  the  space  between  wolfram  and  osmium 
and  the  unknown  element,  which  belongs  in  this  space  of  the 
periodic  system,  thus  should  be  expected  to  have  still  a  higher 
melting  point  than  wolfram,  and  thus  give  a  higher  efficiency  of 
light  production. 

As  metal  alloys  almost  always  have  lower  melting  points  than 
their  most  refractory  element,  very  refractory  compounds  thus 
may  be  expected  only  in  the  compounds  between  the  very  refrac- 
tory elements,  in  which  at  least  one  is  a  metalloid,  that  is,  amongst 
the  carbides  and  borides  and  possibly  silicides  and  titanides. 

37.  Some  of  the  earliest  work  on  incandescent  lamps  was 
carried  out  with  metal  filaments.  Platinum  and  iridium,  how- 
ever, were  not  sufficiently  refractory  to  give  good  efficiencies,  and 
the  very  refractory  metals  were  not  yet  available  in  sufficient 
purity.  A  small  percentage  of  impurities,  however,  very  greatly 
lowers  the  melting  point,  especially  with  metals  of  very  high 
atomic  weight.  For  instance,  wolfram  carbide  contains  only 
3  per  cent  of  carbon  and  97  per  cent  of  wolfram  and  even  0.5  per 
cent  of  carbon  in  wolfram  metal  thus  means  that  16  per  cent  of 
the  metal  consists  of  the  easily  fusible  carbide. 

Very  soon,  therefore,  metal  filaments  were  abandoned  and  car- 
bon used  as  lamp  filament.  While  carbon  is  the  most  refractory 
body,  remaining  solid  up  to  3750  deg.  cent.,  it  was  found  that  the 
carbon  filament  could  not  be  operated  much  above  1800  deg.  cent, 
without  shortening  the  life  of  the  lamp  below  economic  limits  by 
the  evaporation  of  the  carbon  and  the  resulting  blackening  of  the 
lamp  globes.  All  bodies  evaporate  below  their  melting  point. 


TEMPERATURE  RADIATION.  79 

Thus  water  evaporates  considerably  below  the  boiling  point  and 
even  below  the  freezing  point :  ice  and  snow  gradually  disappear 
by  evaporation  even  if  the  temperature  never  rises  above  the 
melting  point.  Considerable  differences,  however,  exist  between 
different  bodies  regarding  their  rate  of  evaporation.  Thus  water 
and  benzine  have  practically  the  same  boiling  point,  but  at  the 
same  distance  below  the  boiling  point,  benzine  evaporates  much 
faster  than  water;  that  is,  has  a  much  higher  vapor  tension. 
Carbon  has  a  very  high  vapor  tension,  that  is,  shows  a  very  rapid 
evaporation  far  below  the  boiling  point,  and  since  in  the  incan- 
descent lamp  the  carbon  vapor  condenses  and  is  deposited  on  the 
globe  and  carbon  is  black,  it  blackens  the  globe  and  obstructs  the 
light.  Also,  the  decrease  of  the  filament  section  by  evaporation 
increases  its  resistance  and  thereby  decreases  the  power  consump- 
tion and  so  still  "further  lowers  the  efficiency.  While,  therefore, 
carbon  remains  solid  up  to  3750  deg.  cent.,  at  about  1800  deg. 
cent,  its  rate  of  evaporation  is  such  as  to  lower  the  candle  power 
of  the  lamp  by  20  per  cent  in  500  hr.  life,  and  at  this  tempera- 
ture it  gives  only  an  output  of  one  candle  power  for  3.1  watts 
input.  Operating  the  carbon  filament  at  higher  temperature 
would  increase  the  efficiency  and  thus  reduce  the  cost  of  energy 
for  the  same  amount  of  light,  but  would  decrease  the  useful  life 
of  the  lamp  and,  therefore,  increase  the  cost  of  lamp  renewals,  and 
the  most  economical  operation,  as  determined  by  balancing  the 
cost  of  lamp  renewals  against  the  cost  of  energy,  is  reached  by 
operating  at  such  temperatures  that  the  candle  power  of  the  lamp 
decreases  by  20  percent  within  500  hr.  life.  The  life  of  a  lamp 
down  to  a  decrease  of  candle  power  by  20  per  cent,  thus,  is  called 
the  useful  life, and  when  comparing  the  efficiencies  of  incandescent 
lamps  it  is  essential  to  compare  them  on  the  basis  of  the  same 
length  of  useful  life:  500  hours  with  the  carbon  filament,  since 
obviously  by  shortening  the  life  higher  efficiencies  could  be 
reached  in  any  incandescent  lamp.  The  operating  temperature 
of  the  carbon  filament  lamp,  thus,  was  limited  by  the  vapor  ten- 
sion of  carbon  and  not  by  its  boiling  point. 

This  limitation  of  carbon  lead  to  the  revival  of  the  metal  fila- 
ment lamps  in  recent  years.  First  arrived  the  osmium  lamp, 
with  1.5  watts  per  candle  power.  The  melting  point  of  osmium  is 
very  high,  but  still  very  much  below  that  of  carbon,  but  the  vapor 
tension  of  osmium  is  very  low  even  close  to  its  melting  point,  so 


80  RADIATION,  LIGHT,  AND  ILLUMINATION. 

that  osmium  could  be  operated  at  temperatures  far  closer  to  its 
melting  point  without  appreciable  evaporation;  that  is,  without 
blackening  and  falling  off  of  candle  power,  or,  in  other  words, 
could  be  run  at  a  temperature  from  which  carbon  was  excluded 
by  its  too  rapid  evaporation.  Osmium,  however,  is  a  very  rare 
metal  of  the  platinum  group,  and  found  only  in  very  limited 
quantities  in  very  few  places  and  is  one  of  those  substances  of 
which  no  search  could  very  greatly  increase  the  supply,  and  while 
one  pound  of  osmium  is  sufficient  for  some  30,000  filaments,  the 
total  amount  of  osmium  which  has  ever  been  found  on  earth 
would  not  be  sufficient  for  one  year's  supply  of  incandescent 
lamps.  Osmium,  therefore,  was  excluded  from  general  use  by  its 
limited  supply. 

The  metal  tantalum  does  not  have  quite  as  high  a  melting  point 
as  osmium,  hence  can  be  operated  only  at  2  watts  per  candle 
power.  Tantalum  also  is  a  very  rare  metal,  but,  unlike  osmium, 
it  is  found  in  very  many  places,  though  in  small  quantities,  but 
it  is  one  of  those  substances,  like  the  rare  earth  metals  used  in 
the  Welsbach  mantel,  of  which  it  seems  that  the  supply  could  be 
infinitely  increased  when  required  by  the  industries  and  the  prices 
thus  would  go  down  with  the  demand,  just  as  has  been  the  case 
with  the  rare  earths  of  the  Welsbach  mantel. 

Last  of  all,  however,  was  made  available  the  most  refractory  of 
all  metals,  wolfram  or  tungsten,  and  as  lamp  filament  permitted 
to  lower  the  specific  consumption  to  1  to  1.25  watts  per 
candle  power,  that  is,  higher  than  any  other  incandescent  radia- 
tor. Wolfram  melts  far  lower  than  carbon,  probably  at  about 
3200  deg.  cent.,  but  far  above  the  temperature  to  which  the  car- 
bon filament  is  limited  by  evaporation,  and  having  practically  no 
vapor  tension  below  its  melting  point,  it  can  be  operated  far 
above  the  temperature  of  the  carbon  filament,  and  thus  gives  a 
much  higher  efficiency.  Tungsten  (or  rather  wolfram,  as  the 
metal  is  called,  tungsten  is  the  name  of  its  ore)  is  a  fairly  common 
metal,  its  salts  are  industrially  used  to  a  very  large  extent  for 
fire-proofing  fabrics  and  its  supply  practically  unlimited. 

These  metal  filaments  thus  differ  from  the  carbon  filament  in 
that  their  temperature  is  limited  by  their  melting  point  and  not 
by  evaporation,  as  is  the  case  with  the  carbon  filament,  and  thus 
their  useful  life  is  usually  ended  by  the  destruction  of  the  filament 
by  melting  through  at  some  weak  spot,  but  not  by  blackening. 


TEMPERATURE  RADIATION.  81 

These  filament  lamps  do  not  blacken  the  globe,  except  when  the 
vacuum  is  defective  or  becomes  defective,  and  by  the  residual 
gases  in  the  lamp  globe  volatile  compounds  are  formed,  as  tungs- 
ten oxide,  which  then  deposits  on  the  globe  and  terminates  the 
life  of  the  lamp.  Even  then  their  blackening  is  characteristically 
different  from  that  of  the  carbon  filament,  in  that  it  occurs  very 
rapidly,  and  the  lamp,  after  running  possibly  for  hundreds  or 
thousands  of  hours  without  blackening,  suddenly  blackens 
within  a  few  days  and  thereby  becomes  inoperative,  while 
with  the  carbon  filament  the  blackening  is  gradual  throughout 
the  life. 

38.  By  the  use  of  these  refractory  metals  the  efficiency  of 
light  production  by  temperature  radiation  has  been  greatly 
increased,  by  permitting  the  use  of  higher  temperatures  in  the 
radiator  than  were  permissible  with  the  carbon  filament  due  to 
its  evaporation.  However,  regarding  the  rate  of  evaporation, 
different  modifications  of  carbon  show  very  different  characteris- 
tics. The  carbon  filaments  first  used  in  incandescent  lamps  were 
made  by  carbonizing  vegetable  fiber,  as  bamboo,  or  by  squirting 
a  solution  of  cellulose  through  a  small  hole  into  a  hardening  solu- 
tion and  carbonizing  this  structureless  horn-like  fiber.  These 
filaments  had  a  very  high  vapor  tension,  thus  could  not  be  run 
as  hot  as  the  modern  carbon  filament  and  so  gave  a  lower  effi- 
ciency. They  are  now  used  only  as  base  filaments,  that  is,  as 
core  on  which  a  more  stable  form  of  carbon  is  deposited.  Such 
a  form  of  carbon  was  found  in  carbon  deposited  on  the  filament 
by  heating  it  in  the  vapor  of  gasolene  or  other  hydrocarbons. 
This  carbon  deposit  is  of  much  lower  electric  resistance  than  the 
base  on  which  it  was  deposited,  its  negative  temperature  coeffi- 
cient of  electric  resistance  is  lower  and  its  vapor  tension  so  much 
lower  as  to  make  it  possible  to  operate  the  lamp  at  a  specific  con- 
sumption of  3.1  watts  per  candle  power.  Of  late  years  a  still 
more  stable  form  of  carbon  has  been  found  in  the  so-called  "me- 
tallic carbon,"  produced  from  the  gasolene  deposited  carbon  shell 
of  the  filament,  by  exposing  it  for  several  minutes  to  a  tempera- 
ture at  the  boiling  point  of  carbon;  that  is,  the  highest  attainable 
temperature  in  an  electric  carbon  tube  furnace.  Hereby  the 
gasolene  deposited  carbon  of  the  filament  shell  — the  inner  base 
does  not  appreciably  change  its  characteristics  —  acquires  metal- 
lic characteristics:  a  low  electric  resistance,  a  positive  tempera- 


82  RADIATION,  LIGHT,  AND  ILLUMINATION. 

ture  coefficient  of  electric  resistance,  metallic  luster  and  elasticity 
and  very  low  vapor  tension,  so  that  it  can  be  run  at  higher  tem- 
perature corresponding  to  a  specific  consumption  of  2.5  to  2.6 
watts  per  candle  power,  with  very  little  blackening.  These  metal- 
lized carbon  filament  lamps  exhibit  characteristics  similar  to  the 
metal  filament  lamps;  their  life  is  largely  limited  by  breakage 
and  not  by  blackening. 

Whether  hereby  the  possibilities  of  carbon  are  exhausted  or 
still  more  stable  forms  of  carbon  will  be  found,  which  permit 
raising  the  filament  temperature  as  near  to  the  boiling  point  of 
carbon  as  the  temperature  of  the  wolfram  filament  is  to  its  melt- 
ing point  *  and  thereby  reach  an  efficiency  superior  to  that  of  the 
tungsten  lamp,  remains  to  be  seen,  but  does  not  appear  entirely 
impossible.  Carbon  exists  in  a  number  of  "allotropic"  modifi- 
cations of  very  different  characteristics  (similar  to  phosphorus  in 
"yellow  phosphorus,"  "red  phosphorus"  and  " metallic  phos- 
phorus") to  a  greater  extent  than  any  other  element,  probably 
due  to  the  tendency  of  the  carbon  atom  to  join  with  other  carbon 
atoms  into  chains  and  rings,  which  tendency  is  the  case  of  the 
infinite  number  of  carbon  compounds.  These  form  two  main 
groups :  the  chain  carbon  derivates  (methane-derivates)  and  the 
ring  carbon  derivates  (benzol  derivates).  The  latter  are  far 
more  stable  at  high  temperatures,  since  the  breakage  of  the  mole- 
cule by  temperature  vibration  is  less  liable  in  a  ring  structure 
than  a  chain :  a  single  break  splits  the  molecule  in  a  chain  forma- 
tion, while  with  a  ring  formation  it  still  holds  together  until  the 
break  closes  again.  Chain  hydrocarbons  at  higher  temperatures 
usually  convert  to  ring  hydrocarbons.  It  is,  therefore,  reasonable 
to  assume  that  the  carbon  skeleton  left  by  the  carbonization  of 
the  hydrocarbons  also  may  exist  in  either  of  the  two  characteris- 
tic atomic  groupings :  as  chain  carbon  and  as  ring  carbon,  and 
that  the  latter  exhibits  a  much  greater  stability  at  high  tempera- 
ture than  the  former,  that  is,  a  lower  vapor  tension.  Cellulose 
is  a  chain  hydrocarbon,  and  as  in  carbonization  it  never  passes 
through  a  fluid  state,  the  molecular  structure  of  its  carbon  atom 
probably  remains  essentially  unchanged.  Thus  the  base  fila- 

*  As  carbon  boils,  at  atmospheric  pressure,  below  its  melting  point,  and  the 
limiting  temperature  is  that  at  which  the  filament  ceases  to  be  solid,  with 
carbon  the  limit  is  the  boiling  point  temperature,  while  with  tungsten  it  is 
the  melting  point. 


TEMPERATURE  RADIATION.  83 

ment  would  be  a  chain  carbon,  and  its  low  stability  and  high  vapor 
tension,  that  is,  the  ease  of  breaking  up  of  the  molecules  by 
evaporation,  thus  would  be  accounted  for. 

A  carbon  compound,  however,  which  passes  through  the  vapor 
state  in  carbonization,  as  the  gasolene  vapor  in  treating  the  car- 
bon filament,  would  as  vapor  at  high  temperature  largely  convert 
into  ring  structures,  that  is,  benzol  derivates,  and  thus  give  a  car- 
bon deposit  consisting  largely  of  molecules  in  which  the  carbon 
atoms  are  grouped  in  rings.  These  molecules,  therefore,  are  more 
stable  at  high  temperatures,  and  thus  exhibit  the  lower  vapor 
tension  shown  by  the  gasolene  deposited  coating  of  the  base 
filament.  This  deposited  carbon,  however,  must  be  expected  to 
have  numerous  side  chains  attached  to  the  ring  nuclei  of  the 
molecules,  and  the  side  chains  are  relatively  easily  split  off  at  high 
temperatures,  as  is  well  known  of  the  benzol  derivates.  As  a 
result  thereof,  this  form  of  carbon,  which  I  may  call  "  interme- 
diate carbon,"  still  shows  a  considerable  vapor  tension,  due  to 
the  side  chains  of  the  ring  structure.  Exposure  to  extremely 
high  temperatures  splits  off  these  side  chains,  which  then  re- 
arrange into  the  only  form  of  carbon  stable  at  these  very  high 
temperatures;  that  is,  ring  structure  and  the  "metallic"  form  of 
carbon  produced  from  the  gasolene  deposited  carbon  by  the  elec- 
tric furnace,  thus  would  be  the  ring  structure  of  the  carbon 
molecule,  that  is,  the  condensation  of  numerous  rings,  similar  to 
that  found  in  anthracene,  etc.  It,  therefore,  would  have  a  very 
high  stability  at  high  temperature;  that  is,  be  difficult  to  split  up 
and  thus  show  the  low  vapor  tension  characteristic  of  the  me- 
tallic carbon.  In  other  words,  the  high  vapor  tension  of  most 
forms  of  carbon  would  be  the  result  of  the  dissociation  of  com- 
plex carbon  molecules  of  chain  structures,  or  of  side  chains  of 
ring  structures,  and  a  carbon  atom  of  complete  ring  structure 
thus  would  only  show  the  vapor  tension  corresponding  to  the 
molecular  weight,  which  is  very  high,  due  to  the  large  number 
of  atoms  in  the  molecule. 

Thus  two  characteristic  allotropic  modifications  of  carbon  may 
exist  besides  the  transparent  carbon  or  diamond : 

(a)^  Chain  carbon:  high  resistance,  negative  temperature  co- 
efficient of  electric  resistance,  non-metallic  character,  high  vapor 
tension  at  moderate  temperature. 

(6).  Ring    carbon:   low    resistance    (within    the    range    of 


84  RADIATION,  LIGHT,  AND  ILLUMINATION. 

metallic  resistivities),  positive  temperature  coefficient  of  re- 
sistance, metallic  character,  low  vapor  tension  at  high  tem- 
peratures. 

The  latter  one,  obviously,  is  best  suited  as  an  incandescent 
radiator. 

It  may  be  possible  to  introduce  into  the  ring  structure  of  the 
carbon  molecule  other  atoms  of  very  refractory  nature,  as  boron, 
titanium,  silicon,  and  by  their  chemical  affinity  still  further  in- 
crease the  stability  of  the  molecule,  so  that  it  does  not  appear 
outside  of  the  possibility  to  find  a  form  of  carbon  which  as  radia- 
tor would  be  superior  to  any  metal  filament. 

39.  Most  bodies  show  the  same  characteristic  in  their  tempera- 
ture radiation;  that  is,  the  total  radiation  varies  in  the  same  man- 
ner with  the  temperature  as  the  fourth  power  of  the  absolute 
temperature.  Thus  the  distribution  of  the  frequencies  in  the 
radiation  is  the  same  for  the  same  temperature,  varies  in  the  same 
manner  with  the  temperature,  so  that  the  distribution  of  the 
radiation  power  between  the  different  frequencies  is  a  charac- 
teristic of  the  temperature,  independent  of  the  material  of  the 
body,  and  can  be  used  for  determining  the  temperature  of  the 
radiator. 

Such  bodies,  therefore,  are  said  to  give  normal  temperature 
radiation. 

Many  bodies  of  normal  temperature  radiation  give  the  same 
intensity,  or  power  of  radiation,  at  the  same  temperature,  that  is, 
have  the  same  radiation  constant  k  in  equation  (1) ;  these  bodies 
are  called  "  black  bodies,"  and  their  radiation  "  black  body  radia- 
tion." Their  radiation  is  the  maximum  temperature  radiation 
given  by  a  body.  Other  bodies  of  normal  radiation  give  a  lower 
intensity  or  radiation,  but  so  that  their  radiation  is  at  any  tem- 
perature and  for  any  frequency  the  same  fraction  of  the  radiation 
of  a  black  body.  Their  radiation,  then,  is  called  "grey  body 
radiation,"  and  they  also  would  follow  the  radiation  law  equa- 
tion (1),  but  with  a  constant  k,  which  is  a  fraction  of  the  constant 
kQ  of  black  body  radiations : 

k  =  bkQ. 

For  temperature  radiation  the  following  law  applies : 
"The  temperature  radiation  of  a  body  is  at  any  temperature 
and  at  any  frequency  the  same  percentage  of  black  body  radiation 


TEMPERATURE  RADIATION.  85 

as  the  absorbed  radiation  of  the  body  is  of  the  total  impinging 
radiation."  (KirchhofTs  law.) 

This  law  relates  the  behavior  of  a  body  towards  radiation 
impinging  upon  it  from  other  bodies,  with  its  behavior  as  radiator. 

A  body  which  absorbs  all  the  impinging  radiation,  that  is,  a 
black  body,  gives  a  maximum  temperature  radiation,  and  this 
radiation,  thus,  has  been  called  the  black  body  radiation.  An 
opaque  grey  body  of  albedo  a,  that  is,  a  body  which  reflects  the 
same  fraction  a  of  the  impinging  radiation  and  thus  absorbs  the 
part  (1  —  a)  of  the  impinging  radiation,  thus  gives  as  radiator 
the  part  (1  -  a)  of  black  body  radiation.  That  is,  its  radiation 
constant  is 

k  =  bk0  =  (1  -  a)  fcc, 

and  the  radiation  constant  of  any  opaque  body, thus,  is  the  radia- 
tion constant  of  the  black  body  multiplied  by  1  minus  its  albedo  a. 

For  a  perfectly  white  or  perfectly  transparent  body,  the  radia- 
tion constant,  thus,  would  be  zero;  that  is,  this  body  would  give 
no  temperature  radiation,  would  not  become  incandescent  at 
high  temperatures. 

40.  A  colored  body  was  defined  as  a  body  which  reflects  or 
transmits  different  fractions  of  the  impinging  radiation  for  dif- 
ferent frequencies.  Such  a  colored  body  usually  absorbs  different 
parts  of  the  impinging  radiation  for  different  frequencies  and  as 
radiator,  then,  would  for  different  frequencies  give  different  frac- 
tions of  black  body  radiation;  that  is,  its  radiation  for  some 
frequencies  would  be  a  greater  part  of  black  body  radiation.  The 
radiation  of  such  a  body  is  called  "colored  body  radiation."  In 
colored  body  radiation  the  distribution  of  intensities  throughout 
the  spectrum,  that  is,  for  different  frequencies,  thus  differs  from 
that  of  the  black  or  grey  body  at  the  same  temperature,  that  is, 
colored  radiation  is  not  normal  radiation  and  thus  also  does  not 
follow  the  temperature  law  equation  (1). 

For  instance,  if  in  Fig.  29, 1  is  the  curve  of  distribution  of  the 
intensity  of  radiation  as  function  of  the  frequency,  at  a  certain 
temperature,  as  the  melting  point  of  tungsten,  for  a  black  body; 
grey  body  radiation  would  be  represented  by  curve  II  or  III,  in 
which  the  ordinates  are  a  constant  fraction  of  those  of  curve  I. 
Curve  II,  for  albedo  a  =  0.3,  has  the  height  1  -  a  =  0.7  times 
that  of  black  body  radiation  I,  that  is,  radiates  70  per  cent  as 


86 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


much  energy,  at  any  temperature  and  of  any  frequency,  as  a  black 
body.  Curve  III  corresponds  to  albedo  a  =  0.6,  or  a  radiation 
constant  1  -  a  =  0.4  times  that  of  the  black  body.  Colored 
body  radiation,  then,  would  be  represented  by  curves  IV  and  V. 
Representing  the  gctave  of  visible  radiation  by  L,  the  area  of 
the  curve  within  the  limits  of  L  to  the  total  area  of  the  radiation 
curve,  gives  the  ratio  of  power  visible  to  total  radiation,  or  the 
"  radiation  efficiency."  As  seen,  this  radiation  efficiency  is  the 
same  for  black  and  grey  bodies,  I,  II,  III,  and  the  only  difference 
between  the  black  and  the  grey  body  is  that  with  the  grey  body 
the  amount  of  light  per  unit  radiating  surface  is  less,  but  the 


7 


\ 


\ 


\ 


\\ 


FIG.  29. 

power  required  to  maintain  the  temperature  is  correspondingly 
less,  hence  the  efficiency  is  the  same  and  merely  a  larger  radiator 
surface  required  to  produce  the  same  amount  of  light ;  the  larger 
the  surface,  the  higher  the  albedo  of  the  radiator.  For  colored 
radiators,  however,  the  radiation  efficiency  may  be  different  and 
frequently  is.  In  the  colored  body  IV,  in  which  the  radiation  in 
the  visible  range  is  a  greater  part  of  the  black  body  radiation  I 
than  in  the  invisible  range,  the  radiation  efficiency  is  greater  than 
that  of  colorless  or  normal  radiation  at  the  same  temperature ; 
that  is,  such  a  colored  body  gives  a  higher  efficiency  of  light 
production  than  corresponds  to  normal  radiation  at  the  same 
temperature.  Such,  for  instance,  is  the  case  with  the  material  of 


TEMPERATURE  RADIATION.  87 

the  Welsbach  mantel.  Inversely,  the  colored  body  V,  in  which 
the  radiation  in  the  visible  range  is  a  lower  percentage  of  black 
body  radiation  than  in  the  invisible  range,  gives  a  lower  efficiency 
of  light  production.  Such,  for  instance,  is  the  case  with  glass, 
which,  therefore,  would  be  an  abnormally  inefficient  incandescent 
light  producer. 

To  illustrate  the  difference  in  the  radiation  of  black  and  grey 
bodies,  I  show  you  here  a  piece  of  graphite  rod,  around  which  a 
strip  of  platinum  foil  is  wrapped  in  an  open  spiral  and  then  it  is 
enclosed  in  a  transparent  quartz  tube.  Heating  it  in  the  bunsen 
flame,  you  see  the  graphite  becomes  bright  red,  while  the  platinum 
foil  surrounding  it  is  far  less  luminous  and  the  quartz  tube  is  not 
luminous  at  all,  though  all  three  have  practically  the  same  temper- 
ature, or  if  anything,  the  outer  quartz  tube  is  the  hottest,  the 
interior  graphite  rod  the  coolest.  Still,  the  graphite  gives  the 
greatest  amount  of  light :  graphite  is  a  black  body  and  thus  gives 
maximum  radiation;  the  platinum  as  a  grey  body  gives  less  radia- 
tion at  the  same  temperature  and  the  quartz  as  a  transparent 
body  which  absorbs  almost  no  radiation,  thus,  also,  gives  out 
almost  no  radiation,  that  is,  does  not  become  luminous  at  a 
temperature  at  which  the  graphite  is  bright  red. 

I  now  drop  a  small  platinum  spiral  into  a  mixture  of  the  nitrates 
of  thoria  and  ceria  (the  rare  earths  of  the  Welsbach  mantel),  and 
then  immerse  it  in  the  bunsen  flame.  The  nitrates  convert  to 
oxides,  which  fluff  out  into  a  very  light  and  porous  mass,  which 
you  see  glow  in  a  very  intense,  slightly  greenish  light,  far  brighter 
than  the  platinum  wire  immersed  in  the  same  flame.  The  dis- 
tribution of  intensity  of  this  radiation  differs  from  that  corre- 
sponding to  any  temperature,  and  the  percentage  of  visible 
radiation,  especially  from  the  center  of  the  visible  spectrum 
(greenish  yellow) ,  is  abnormally  large.  This,  therefore,  is  a  colored 
radiator,  giving  a  higher  radiation  efficiency  than  the  normal 
temperature  radiation. 

A  radiation  which  does  not  follow  the  temperature  law  of 
normal  radiation  as  regard  to  the  distribution  of  intensity  with 
the  frequency,  is  called  " selective  radiation."  Colored  body 
radiation,  thus,  is  selective  radiation. 

In  regard  to  their  reaction  on  light  impinging  on  them,  in  reflect- 
ing or  transmitting  it,  most  bodies  are  more  or  less  colored  and 
colorless  bodies:  black,  grey,  white,  transparent,  the  exception. 


88  RADIATION,  LIGHT,  AND  ILLUMINATION. 

Regarding  the  temperature  radiation  produced  by  the  body  as 
radiator,  most  bodies  are  colorless,  black  or  grey  bodies,  that  is, 
give  normal  radiation  or  nearly  so,  and  colored  or  selective  radia- 
tion of  appreciable  intensity  is  the  exception. 

Obviously,  no  perfectly  black,  or  even  perfectly  colorless  radia- 
tor exists,  but  even  carbon  shows  a  slight  selectivity,  a  slightly 
greater  intensity  of  radiation  at  the  red  end  of  the  spectrum  than 
corresponds  to  the  temperature. 

Perfectly  black  body  radiation,  "however,  is  the  radiation  at 
the  inside  of  a  hollow  body  of  uniform  temperature,  and  the 
laws  of  black  body  radiation,  thus,  are  studied  on  the  radiation 
in  the  interior  of  a  closed  shell  with  opaque  walls  of  uniform 
temperature. 

In  the  interior  of  such  a  hollow  body  of  uniform  temperature 
every  surface  element  radiates  to  every  other  element  and  receives 
radiation  from  every  other  surface  element,  that  is,  the  surface 
element  Al  receives  as  much  radiation  from  element  A2  as  ele- 
ment A2  receives  from  Ar 

Of  the  radiation  received  by  a  surface  element  Al  by  the  radia- 
tion law,  that  part  which  exists  in  the  radiation  produced  by  A1 
is  absorbed,  that  part  which  does  not  exist  in  the  temperature 
radiation  of  Av  is  reflected,  and  the  total  radiation  issuing  from 
Ax,  the  radiation  produced  by  it  plus  that  reflected  by  it, together, 
thus,  make  up  complete  black  body  radiation.  If,  then,  the  hol- 
low radiator  is  a  black  body,  it  absorbs  all  the  impinging  radia- 
tion, reflects  none,  and  the  radiation  issuing  from  it  thus  is  the 
black  body  radiation  produced  by  it.  If  the  radiator  is  not 
a  black  body,  buj  a  grey  or  a  colored  body,  of  any  frequency  of 
radiation,  for  which  it  has  the  albedo  a,  only  the  part  (1  —  a) 
is  produced  by  it,  but  the  part  a  of  the  impinging  radiation  of 
this  frequency  is  reflected,  and  the  total  radiation  of  this  fre- 
quency, thus,  still  is  unity,  that  is,  back  body  radiation. 

Obviously,  the  body  cannot  be  perfectly  closed,  but  must 
contain  an  opening,  through  which  the  interior  radiation  is 
observed,  but  if  this  opening  is  sufficiently  small  it  introduces  no 
appreciable  error. 

The  production  of  black  body  radiation  from  the  interior  of  a 
hollow  body  obviously  requires  that  the  walls  of  the  body  be 
opaque;  that  is,  that  all  the  radiation  produced  inside  of  it  is 
either  absorbed  or  reflected,  and  also  depends  on  the  condition 


TEMPERATURE  RADIATION.  89 

that  all  the  frequencies  of  black  body  radiation  are  present,  since 
evidently,  no  frequency  which  is  entirely  absent  in  the  radiation 
of  the  body  could  be  produced  by  reflection.  Furthermore,  all 
the  radiation  must  be  temperature  radiation,  that  is,  no  lumines- 
cence exist  in  the  interior  of  the  body.  These  requirements  are 
easily  fulfilled,  except  at  extremely  high  temperatures. 

41.  The  radiation  laws  offer  a  means  of  measuring  tempera- 
ture, and  the  only  means  for  those  very  high  temperatures  where 
the  gas  thermometer  (that  is,  the  measurement  of  temperature  by 
the  expansion  of  a  gas)  and  the  thermo-electric  couple  or  the 
resistance  pyrometer  cannot  longer  be  used,  as  no  material  exists 
which  remains  solid  at  temperatures  such  as  those  of  electric 
furnaces,  etc. 

As  the  total  intensity  of  the  radiation  varies  with  the  fre- 
quency, and  the  ratio  of  the  intensity  of  radiation  of  any  definite 
frequency  to  the  total  radiation,  or  the  ratio  of  intensities  at 
two  different  frequencies  of  radiation,  is  a  function  of  the  tem- 
perature, either  can  be  used  for  measuring  the  temperature. 

For  instance,  measuring  the  intensity  of  the  total  radiation  — 
which  in  vacuum  enclosed  radiators  as  incandescent  lamp  fila- 
ments is  done  by  measuring  the  power  input  —  gives  the  tem- 
perature if  the  body  is  a  black  body  and  its  radiating  surface 
measured.  If  one  temperature  is  known,  as,  for  instance,  by  the 
melting  point  of  some  substance,  by  comparing  the  total  radia- 
tion power  with  that  at  the  known  temperature,  other  tempera- 
tures can  be  measured. 

Determining  the  ratio  of  the  power  of  the  visible  radiation, 
and  that  of  the  total  radiation  — that  is,  the  radiation  efficiency 
—  thus  gives  the  temperature  for  black  bodies  as  well  as  grey 
body  radiators. 

By  comparing  the  intensity  of  any  two  radiations  we  get  the 
temperature.  This  can  be  done  very  easily  by  using  two  wave 
lengths  of  radiation  in  the  visible  range.  For  instance,  the  ratio 
of  the  intensity  of  the  yellow  and  the  blue  radiation  gives  the 
temperature.  Resolving,  then,  the  radiation  by  a  prism  P  in 
Fig.  30,  into  a  spectrum,  and  by  a  shutter  $t  cutting  out  a 
definite  width  of  yellow  and  of  blue  light,  and  combining  these 
again  by  the  mirror  Ml  and  M2  we  get  a  resultant  green  color 
which  is  intermediate  between  yellow  and  blue,  and  the  nearer  to 
the  blue,  the  higher  the  temperature.  Arranging,  then,  the  mov- 


90  RADIATION,  LIGHT,  AND  ILLUMINATION. 

able  shutter  S2  below  Sl  with  a  single  opening,  we  can  by  it  cut 
out  a  single  green  color,  and  by  moving  the  shutter  S2  bring  this 
to  coincidence  in  shade  with  the  resultant  color  of  shutter  Sv  and 
the  position  of  the  shutter  S2  then  measures  the  temperature. 
The  scale  of  such  a  direct  vision  pyrometer  may  either  be  calcu- 
lated from  the  radiation  laws,  or  it  may  be  calibrated  by  some 
known  temperatures,  as  the  melting  points  of  gold,  platinum, 
boiling  point  of  carbon,  etc. 

A  number  of  types  of  such  visual  pyrometers  have  been  devel- 
oped, and  are  very  convenient. 

Their  limitation,  obviously,  is  that  they  apply  only  when  the 
radiation  is  normal  temperature  radiation,  but  give  wrong  results 
where  colored  radiation  or  luminescence  is  present.  Thus  the 


FIG.  30. 

radiation  given  by  the  interior  of  a  closed  body  of  uniform  tem- 
perature ceases  to  be  black  body  radiation  if  the  interior  is  filled 
with  luminous  vapors,  as  is  frequently  the  case  in  the  interior  of 
electric  furnaces.  For  instance,  using  such  a  visual  pyrometer 
for  the  interior  of  the  carbon  tube  furnace  used  for  metallizing 
carbon  filaments  gives,  frequently,  quite  impossible  results,  tem- 
peratures above  those  of  the  sun,  due  to  the  error  caused  by  the 
luminescent  silicon  vapor  filling  the  tube. 

The  errors  of  temperature  measurements  by  radiation  are  the 
greater  the  nearer  together  the  radiation  frequencies  are  which 
are  used  for  the  measurement,  hence  are  greatest  with  the  visual 
pyrometers,  least  in  the  methods  based  on  the  total  radiation 
power. 

42.  In  the  temperature  radiation  of  a  colored  body  the  ratio 
of  the  intensity  of  the  radiation  to  that  of  a  black  body  of  the 


TEMPERATURE  RADIATION.  91 

same  temperature  is  different  for  different  frequencies  of  radia- 
tion, and  the  average  wave  length  of  radiation  and  the  total 
intensity  of  radiation  of  a  colored  body  thus  do  not  vary  with  the 
temperature  in  the  same  manner  as  is  the  case  with  the  black  and 
the  grey  body,  that  is,  the  normal  radiation.  The  intensity  of 
colored  body  radiation  at  any  frequency  cannot  exceed  the  inten- 
sity of  radiation  of  a  black  body  at  the  same  temperature  and 
frequency,  since  the  radiation  of  the  black  body  is  the  maximum 
temperature  radiation  at  any  temperature  and  frequency. 

A  body  which  gives  at  any  frequency  a  greater  intensity  of 
radiation  than  a  black  body  of  the  same  temperature  is  called 
luminescent,  that  is,  said  to  possess  "heat  luminescence."  Char- 
acteristic of  heat  luminescence,  thus,  is  an  excess  of  the  intensity 
of  radiation  over  that  of  a  black  body  of  the  same  temperature  for 
some  frequency  or  range  of  frequencies,  and  the  color  of  lumin- 
escence is  that  of  the  radiation  frequencies  by  which  the  lumin- 
escent body  exceeds  the  black  body. 

It  is  not  certain  whether  such  heat  luminescence  exists. 

The  high  efficiency  of  light  production  of  the  Welsbach  man- 
tel, of  the  lime  light,  the  magnesium  flame,  the  Nernst  lamp,  etc., 
are  frequently  attributed  to  heat  luminescence. 

The  rare  oxides  of  the  Welsbach  mantel,  immersed  in  the 
bunsen  flame,  give  an  intensity  of  visible  radiation  higher  than 
that  of  a  black  body,  as  a  graphite  rod,  immersed  in  the  same 
flame,  and  if  we  assume  that  these  oxides  are  at  the  same  tempera- 
ture as  the  flame  in  which  they  are  immersed,  their  light  must  be 
heat  luminescence  and  not  colored  radiation,  as  the  latter  can- 
not exceed  that  of  a  black  body.  It  is  possible,  however,  that 
these  oxides  are  at  a  higher  temperature  than  the  flame  surround- 
ing them,  and  as  the  radiation  intensity  of  a  black  body  rapidly 
rises  with  the  temperature,  the  light  radiation  of  the  rare  oxides, 
while  greater  than  that  of  a  black  body  of  the  flame  temperature, 
may  still  be  less  than  that  of  a  black  body  of  the  same  tempera- 
ture which  the  oxides  have,  and  their  radiation,  thus,  colored 
temperature  radiation  and  not  luminescence.  Very  porous 
materials,  as  platinum  sponge,  absorb  considerable  quantities  of 
gases,  and  by  bringing  them  in  close  contact  with  each  other  in 
their  interior  cause  chemical  reaction  between  them,  where  such 
can  occur,  and  thus  heat  and  a  temperature  rise  above  surround- 
ing space.  Thus  platinum  sponge,  or  fine  platinum  wire,  immersed 


92  RADIATION,  LIGHT,  AND  ILLUMINATION. 

in  a  mixture  of  air  and  alcohol  vapor  at  ordinary  temperature, 
becomes  incandescent  by  absorbing  alcohol  vapor  and  air  and 
causing  them  to  combine.  The  oxides  of  the  Welsbach  mantel, 
as  produced  by  the  deflagration  of  their  nitrates,  are  in  a  very 
porous  state,  and  thus  it  is  quite  likely  that  in  the  bunsen  flame 
they  absorb  gas  and  air  and  cause  them  to  combine  at  a  far  more 
rapid  rate  than  in  the  flame,  and  thereby  rise  above  the  flame 
temperature.  An  argument  in  favor  of  this  hypothesis  is,  that 
these  oxides,  when  immersed  in  the  bunsen  flame  in  close  contact 
with  a  good  heat  conductor,  as  platinum,  and  thereby  kept  from 
rising  above  the  flame  temperature,  do  not  show  this  high  lumi- 
nosity. I  have  here  a  small,  fairly  closely  wound  platinum  spiral 
filled  with  these  oxides.  Immersing  it  in  the  bunsen  flame  you 
see  the  oxides  and  the  platinum  wire  surrounding  them  glow  with 
the  same  yellow  light,  but  see  none  of  the  greenish  luminosity 
exhibited  by  the  oxide  when  free  in  the  flame,  except  at  a  few 
points  at  which  the  oxide  projects  beyond  and  is  not  cooled  by 
the  platinum  spiral.  The  absence  of  a  high  selective  luminosity 
of  these  oxides,  when  heated  electrically  in  a  vacuum  or  in  an 
inactive  gas,  also  points  this  way.  The  gradual  decay  of  the 
luminosity  shown  by  such  radiators  may  be  due  to  their  becoming 
less  porous,  by  sintering  —  this  would  account  for  the  very  rapid 
decay  of  the  light  of  the  lime  cylinder  in  the  hydro-oxygen  flame, 
and  the  very  small  decay  of  the  more  refractory  oxides  in  the 
Welsbach  mantel  —  but  it  also  may  be  the  general  characteristic 
of  luminescence,  as  we  have  found  in  the  discussion  of  fluorescence 
and  phosphorescence. 

In  favor  of  heat  luminescence  as  the  cause  of  the  very  high  effi- 
ciency of  these  radiators  is,  however,  the  similarity  of  the  con- 
ditions under  which  it  occurs,  with  those  we  find  in  fluorescence 
and  phosphorescence.  Just  as  neither  calcium  sulphide  nor  zinc 
silicate  nor  calcium  carbonate  are  fluorescent  or  phosphorescent, 
when  chemically  pure,  but  the  fluorescence  and  phosphorescence 
are  due  to  the  presence  of  a  very  small  quantity  of  impurities,  as 
manganese,  so  the  pure  oxides,  thoria,  erbia,  ceria,donot  give  very 
high  luminosity  in  the  bunsen  flame,  but  the  high  luminosity  is 
shown  by  thoria  when  containing  a  very  small  percentage  of  other 
oxides. 

While  the  existence  of  heat  luminescence  in  these  rare  oxides 
is  not  certain,  no  theoretical  reason  exists  against  it,  as  at  ordi- 


TEMPERATURE  RADIATION.  93 

nary  temperature  we  have  in  phosphorescence  the  same  phenome- 
non of  the  production  of  a  radiation  exceeding  in  intensity  that 
of  a  black  body  of  the  same  temperature:  the  black  body  radia- 
tion at  ordinary  temperature  contains  no  visible  rays,  while  that 
of  a  phosphorescent  body  does.  Heat-luminescence,  thus,  may 
be  considered  as  fluorescence  at  high  temperature. 

However,  to  some  extent,  the  question  of  the  existence  of  heat 
luminescence  depends  upon  the  definition  of  luminescence,  and 
any  colored  radiation  may  be  considered  as  heat  luminescence  of 
a  grey  body.  For  instance,  the  radiation  represented  by  curves 
IV  and  V  of  Fig.  29,  may  be  considered  as  colored  temperature 
radiation,  as  they  are  below  black  body  radiation,  curve  I.  But 
as  they  exceed  at  some  frequencies  the  curves  of  grey  body 
radiation  II  and  III,  they  may  also  be  considered  as  heat  lumi- 
nescence of  a  grey  body.  If,  then,  we  compare  such  curves  of 
selective  radiation,  IV  and  V,  with  normal  temperature  radiation 
of  the  same  total  intensity  — that  is,  with  a  grey  body  radiation 
of  the  same  power  at  the  same  temperature  —  all  such  selective 
radiation  can  be  considered  as  heat  luminescence. 

While  the  term  " luminescence"  is  usually  applied  only  to 
abnormally  high  radiation  in  the  visible  range,  in  its  general 
physical  meaning  it  applies  to  abnormal  radiation  of  any  fre- 
quency range,  and  curve  V  in  Fig.  29,  for  instance,  would  be  the 
curve  of  a  grey  body,  which  luminesces  in  the  ultra-red,  while 
curve  IV  would  be  that  of  a  grey  body,  in  which  the  heat  lumi- 
nescence is  in  the  visible  range. 

In  general,  however,  it  is  preferable  to  consider  as  luminescence 
only  such  radiation  as  exceeds  the  black  body  radiation  of  the 
same  temperature,  and  this  will  be  done  in  the  following,  while 
radiations  which  differ  in  their  frequency  distribution  from  the 
black  body,  without  exceeding  it  in  intensity,  are  considered  as 
colored  body  radiations. 


LECTURE  VI. 

LUMINESCENCE. 

43.  All  methods  of  producing  radiation,  and  more  particularly 
light,  other  than  the  temperature  radiation  or  incandescence,  are 
generally  comprised  by  the  name  luminescence.  Some  special 
cases  of  luminescence  have  already  been  discussed  in  the  phe- 
nomena of  fluorescence  and  phosphorescence,  represented  by  the 
conversion  of  the  radiation  absorbed  by  a  body  into  radiation  of 
a  different  wave  length. 

Usually  luminescence  at  ordinary  temperature,  or  at  moderate 
temperatures,  that  is,  temperatures  below  incandescence,  is  called 
fluorescence  or  phosphorescence. 

Fluorescence  and  Phosphorescence. 

Fluorescence  is  the  production  of  radiation  from  the  energy 
supplied  to  and  absorbed  by  the  fluorescent  body,  while  phos- 
phorescence is  the  production  of  radiation  from  the  energy  stored 
in  the  phosphorescent  body.  This  energy  may  be  derived  from 
internal  changes  in  the  body,  as  slow  combustion,  or  may  have 
been  received  by  the  body  at  some  previous  time  —  as  by 
exposure  to  light  a  calcium  sulphide  screen  absorbs  the  energy 
of  incident  radiation,  stores  it  in  some  form,  and  afterwards 
radiates  it. 

Fluorescence  and  phosphorescence  usually  occur  simulta- 
neously :  the  energy  supplied  to  such  a  luminescent  body  brings 
about  certain  changes  in  the  body  —  as  vibrations  of  the  atoms, 
or  whatever  it  may  be  —  which  cause  the  body  to  send  out  radia- 
tion. As  long  as  this  energy  is  supplied,  the  radiation  of  the 
body  continues,  that  is,  it  fluoresces.  The  changes  in  the  body 
which  make  it  luminesce,  represent  energy  storage  —  the  kinetic 
energy  of  the  luminescent  vibration,  etc.  —  and  when  the  energy 
supply  to  the  body  ceases,  the  radiation  issuing  from  the  body 
does  not  instantly  cease,  but  continues,  with  gradually  decreasing 
intensity,  until  the  stored  energy  is  dissipated :  the  body  phos- 

94 


LUMINESCENCE.  95 

phoresces.  Inversely,  fluorescent  radiation  probably  does  not 
appear  instantly  at  full  intensity,  as  energy  has  first  to  be  stored. 
The  persistence  of  the  luminescence  after  the  power  supply  has 
stopped,  as  phosphorescence,  is  very  short,  except  with  a  few 
substances,  where  it  lasts  for  days.  Where  the  energy  of  phos- 
phorescent radiation  is  supplied  by  the  energy  of  chemical 
change  in  the  body  —  as  with  yellow  phosphorus  —  obviously 
the  phosphorescence  persists  as  long  as  these  chemical  changes 
can  occur. 

The  different  forms  of  luminescence  may  be  distinguished  by 
the  character  of  the  energy  which  is  converted  into  radiation. 

The  conversion  of  radiation  energy  into  radiation  of  different 
wave  length,  either  immediately,  or  after  storage  in  the  body, 
thus  may  be  called  radio-fluorescence  and  radio-phosphorescence. 
It  was  discussed  in  Lecture  II. 

The  same  bodies,  exposed  to  an  electric  discharge  in  a  vacuum 
(Geissler  tube  or  Crooke  tube)  show  electro-luminescence,  fluores- 
cence as  well  as  phosphorescence,  and  usually  with  the  same 
color  as  in  radio-luminescence. 

Thermo-luminescence  is  exhibited  by  some  materials,  as  the 
violet  colored  crystals  of  fluorite  (CaFl2),  which,  when  slightly 
warmed,  luminesce  — it  is  this  which  gave  the  name  "fluores- 
cence" to  the  phenomenon. 

Some  solutions,  when  crystallizing,  show  light  during  the 
formation  of  crystals,  and  thus  may  be  said  to  exhibit  a  physical 
phosphorescence. 

Chemical  phosphorescence  is  exhibited  by  yellow  phosphorus 
and  its  solutions,  which  in  the  air  glow  by  slow  combustion,  at 
ordinary  atmospheric  temperature.  As  the  ignition  point  of 
phosphorus,  that  is,  the  temperature  where  it  spontaneously 
ignites,  is  little  above  atmospheric  temperature,  the  chemical  phos- 
phorescence of  phosphorus  occurs  at  temperatures  a  few  degrees 
below  ignition;  it  ceases,  however,  at  very  low  temperature. 

The  chemical  luminescence,  as  shown  by  phosphorus,  is  not 
an  exceptional  phenomenon,  but  many  substances  exhibit  chemi- 
cal phosphorescence  at  temperatures  a  few  degrees  below  their 
ignition  temperature,  as  the  result  of  slow  combustion.  With 
those  substances  which  have  an  ignition  point  above  incandes- 
cence, this  cannot  be  observed,  but  it  is  observed,  for  instance, 
in  carbon  bisulphide,  CS2,  which  ignites  spontaneously  at  about 


96  RADIATION,  LIGHT,  AND  ILLUMINATION. 

180  deg.  cent.,  and  a  few  degrees  below  this  temperature  phos- 
phoresces in  air,  by  slow  combustion. 

A  biological  phosphorescence  is  shown  by  many  forms  of  life: 
some  bacilli  of  putrefaction  phosphoresce,  and  are  the  cause  of 
the  faint  glow  occasionally  observed  in  decaying  food,  especi- 
ally fishes.  Amongst  insects,  numerous  sea  animals  of  dif- 
ferent classes,  especially  deep-sea  animals,  phosphorescence  is 
frequently  met,  but  its  origin,  that  is,  the  mechanism  of  light 
production  by  the  firefly,  etc.,  is  still  unknown. 

When  splitting  a  sheet  of  mica,  or  shaking  a  well-exhausted 
tube  containing  mercury,  flashes  of  light  are  seen  in  the  darkness. 
This,  however,  is  not  real  phosphorescence  but  due  to  electrostatic 
flashes  of  frictional  electricity. 

The  light  given  by  fluorescence  and  phosphorescence  of  solids 
or  liquids,  gives  a  continuous  spectrum,  that  is,  is  a  mixture  of  all 
frequencies,  just  as  is  the  case  with  temperature  radiation;  it 
differs,  however,  from  temperature  radiation  by  the  distribu- 
tion of  the  energy  in  the  spectrum,  which  is  more  or  less  charac- 
teristic of  the  luminescent  body,  and  to  some  extent,  also,  of  the 
method  of  exciting  the  luminescence.  Thus  crystalline  calcium 
tungstate,  W04Ca,  fluoresces  white  in  the  X-ray,  light  blue  with 
ultra-violet  light;  the  aniline  dye,  rhodamine,  6  G,  in  alcoholic 
solution  fluoresces  green  in  daylight,  crimson  in  the  light  of  the 
mercury  lamp;  willemite  (calcium  silicate)  shows  a  maximum 
fluorescent  radiation  in  the  green,  some  chalcites  in  the  red,  etc. 

So  far,  fluorescence  and  phosphorescence  nave  not  yet  found 
any  extended  industrial  application. 

44.  Some  of  the  characteristic  forms  of  luminescence  at  higher 
temperatures  are  pyro-luminescence,  chemical-luminescence,  and 
electro-luminescence. 

As  pyro-luminescence  or  heat-luminescence,  must  be  considered  all 
radiation,  produced  by  heat,  which  exceeds  at  some  wave  length 
the  intensity  of  the  black  body  radiation  at  the  same  temperature. 

Whether  real  pyro-luminescence  exists,  is  uncertain,  but  by  an 
extension  of  the  definition  any  colored  temperature  radiation 
may  be  considered  as  heat  luminescence  of  a  grey  body  of  an 
albedo  which  as  normal  temperature  radiation  would  give  the 
same  total  radiation  at  the  same  temperature  as  the  colored 
radiator.  Heat  luminescence  has  been  discussed  already  under 
colored  radiation. 


LUMINESCENCE.  1 97 

Chemical  Luminescence. 

Whenever  intense  chemical  changes  take  place  at  higher  tem- 
perature, luminescence  frequently  occurs.  I  have  here  an  ordi- 
nary, non-luminous  bunsen  flame.  I  dip  a  platinum  wire  into  a 
solution  of  lithium  chloride,  LiCl,  and  then  hold  it  into  the  lower 
edge  of  the  flame:  the  flame  colors  a  bright  red,  and  through  the 
spectroscope  you  see  a  bright  deep  red  line  and  a  less  bright 
orange  line,  the  spectrum  of  Li.  After  a  little  while,  the  color- 
ing disappears  by  the  LiCl  evaporating  from  the  wire,  and  the 
flame  again  becomes  non-luminous.  I  repeat  the  same  experi- 
ment, but  dip  the  platinum  wire  into  sodium  chloride,  NaCl, 
solution,  and  you  see  the  flame  colored  brightly  yellow,  and  the 
spectroscope  shows  one  yellow  line,  the  sodium  line  D.  Dipping 
the  platinum  wire  into  thallium  chloride,  T1C1,  I  color  the  flame 
a  bright  deep  green,  the  characteristic  Tl  spectrum,  which  has  one 
bright  green  line.  As  you  see,  the  green  coloring  disappears 
more  rapidly  than  the  yellow  did,  and  the  flame  turns  yellow; 
the  Tl  salt  is  more  volatile  than  the  sodium  salt,  evaporates  more 
rapidly,  and  as  it  contains  some  Na  as  impurity,  the  latter  be- 
comes visible  as  yellow  flame  coloring  after  the  Tl  has  evap- 
orated. 

In  the  bunsen  flame  these  salts  are  evaporated,  split  up  into 
their  elements  by  the  flame  gases,  and  recombine,  and  by  these 
chemical  changes  the  atoms  of  Li,  Na  or  Tl  are  set  in  vibration, 
and  as  vapors,  being  free  to  vibrate  without  mutual  interference, 
they  vibrate  with  their  characteristic  frequency,  that  is,  give  a 
definite  frequency  and  thus  color  of  the  light,  independent  of  the 
temperature;  if  we  introduce  the  same  salts  into  the  carbon  arc 
we  get  the  same  color  and  the  same  spectrum  lines,  only  much 
brighter,  as  at  the  much  higher  temperature  of  the  arc  flame  the 
vibration  is  far  more  intense;  but  it  is  of  the  same  frequency,  and 
in  this  respect  essentially  differs  from  temperature  radiation 
which  varies  in  frequency  with  the  temperature. 

In  the  same  manner  by  introducing  Sr,  Ba  or  Ca  salts  in 
the  bunsen  flame,  the  flame  is  colored  with  other  character- 
istic colors;  bright  red,  green,  orange  The  spectroscope  shows 
in  every  case  a  spectrum  having  a  number  of  definite  lines 
which  are  brightest  and  most  numerous  in  the  red  for  Sr,  in  the 
green  for  Ba,  and  in  the  orange  yellow  for  Ca.  In  general, 


98  RADIATION,  LIGHT,  AND  ILLUMINATION. 

metal  spectra  show  a  number,  frequently  very  many  lines  in 
the  visible  range. 

As  Sr,  Ba,  Ca,  are  much  less  volatile  than  Li,  Na,  Tl,  to  get 
good  effects  in  the  bunsen  flame,  instead  of  the  chlorides,  the 
nitrates,  or  preferably  the  chlorates  or  perchlorates  are  used, 
which  are  more  unstable,  and  thus  easier  split  up  and  carried  into 
the  flame.  At  the  much  higher  temperature  of  the  carbon  arc, 
the  chlorides,  or  even  the  still  more  refractory  oxides  are  used. 

Chemical  luminescence  is  used  industrially  in  fireworks  and 
colored  signal  lights;  salts  of  these  metals  with  acids  which  con- 
tain a  large  amount  of  easily  split  off  oxygen,  as  nitrates,  or  more 
commonly  chlorates  and  perchlorates,  are  mixed  with  some  com- 
bustible material,  as  charcoal,  sugar,  sulphur,  antimony  sulphide, 
etc.  When  ignited,  the  combustible  burns  with  the  oxygen 
given  off  by  the  nitrates  or  chlorates,  and  in  the  focus  of  this 
intense  chemical  action,  intense  luminescence  of  the  metal  is 
produced.  Thus  Sr  gives  a  bright  red,  Ba  a  green,  Ca  an  orange 
yellow,  copper  ammon  a  blue  coloring. 

Electro-luminescence  of  Gases  and  Vapors. 

45.  Industrially  this  is  the  most  important  form  of  lumines- 
cence. Solids  and  liquids  can  be  made  to  luminesce  only  indi- 
rectly by  exposure  to  electric  discharges,  as  electrical  fluorescence. 
Gases,  however  — and  under  gases  here  and  in  the  following  we 
include  vapors  as,  for  instance,  the  carbon  vapor,  which  is  the 
conductor  in  the  carbon  arc  —  become  electro-luminescent  by 
being  used  as  conductors  of  the  electric  current.  It  is  a  charac- 
teristic of  electric  conduction  of  the  gases  that  this  conduction  is 
accompanied  by  the  production  of  radiation,  and  in  the  electric 
conduction  of  gases  we  thus  find  the  means  of  a  more  direct 
conversion  of  electric  energy  into  radiation,  and  thus  into  light. 
It  is,  therefore,  in  this  direction  that  a  radical  advance  in  the 
efficiency  of  light  production  would  be  possible,  and  the  subject 
of  electric  conduction  of  gases  (including  vapors)  thus  is  of  the 
highest  importance. 

Two  forms  of  electric  conduction  in  gases  exist:  disruptive 
conduction,  as  represented  by  the  Geissler  discharge  or  the  elec- 
trostatic spark,  and  continuous  conduction,  as  represented  by  the 
electric  arc. 


LUMINESCENCE.  99 

Disruptive  Conduction. 

In  disruptive  conduction  the  conductor  is  the  gas  which  fills  the 
space  between  the  terminals,  and  in  carrying  the  current  is 
made  luminous.  The  color  of  the  light  and  its  spectrum  is  that 
of  the  gas  which  fills  the  space,  and  the  electrode  material  has  no 
effect  on  the  phenomenon,  is  immaterial  (in  the  Geissler  tube, 
or  the  spark  gap,  any  material  may  be  used  as  terminal,  if  it 
•otherwise  is  suitable,  that  is,  is  not  destroyed  by  whatever  heat 
is  produced  at  the  terminals,  or  by  the  chemical  action  of  the  gas 
in  the  space,  etc.)  usually,  however,  the  electrodes  gradually  dis- 
integrate in  disruptive  conduction. 

Disruptive  conduction  is  discontinuous;  that  is,  no  current 
exists  below  a  certain  definite  voltage,  while  above  this  voltage 
there  is  current.  The  voltage  at  which  conduction  begins  is 
called  the  disruptive  voltage.  It  is  the  minimum  supply  voltage  at 
•  which  current  exists :  if  the  supply  voltage  rises  above  this  value 
there  is  current;  if  it  drops  below  the  disruptive  voltage  the 
current  ceases,  but  begins  again  spontaneously  as  soon  as,  the 
voltage  rises  above  the  disruptive  value.  Disruptive  conduction 
thus  occurs  equally  well  with  unidirectional,  with  alternating, 
or  with  oscillating  currents.  It  is  best  studied  with  alternating 
or  oscillating  voltage  supply,  as  with  a  steady  unidirectional 
voltage,  the  disruptive  conduction,  that  is,  conduction  by  the 
gas  filling  the  space  between  the  electrodes,  tends  to  change  to 
continuous  conduction,  by  vapors  forming  at  the  negative  elec- 
trode and  gradually  bridging  the  space  between  the  electrodes, 
and  thereby  replacing  the  gas  which  fills  the  space,  by  the  elec- 
trode vapor  as  conductor.  This  is  usually  expressed  by  saying: 
the  electrostatic  spark  between  two  terminals  starts,  or  tends  to 
start,  an  arc. 

Disruptive  conduction,  thus,  does  not  follow  Ohm's  law;  it  is 
zero  below  the  disruptive  voltage,  while  with  a  supply  voltage 
exceeding  the  disruptive  voltage  of  the  gas  between  the  terminals, 
current  exists,  but  the  terminal  voltage  is  apparently  indepen- 
dent of  the  current,  that  is,  if  the  other  conditions  as  temperature, 
gas  pressure,  etc.,  remain  the  same,  the  terminal  voltage  of  the 
Geissler  tube  or  the  spark  gap  remains  the  same  and  independent 
of  the  current,  and  the  current  is  determined  by  the  impedance 
between  the.  Geissler  tube  or  spark  gap  and  the  source  of 


100  RADIATION,  LIGHT,  AND  ILLUMINATION. 

e.m.f.,  or  by  the  available  power  of  the  supply  source.  A  Geissler 
tube,  thus,  cannot  be  operated  directly  on  a  constant  potential 
supply  of  unlimited  power,  but  requires  a  current  limiting  im- 
pedance in  series  with  it,  or  a  source  of  limited  power,  that 
is,  a  source  in  which  the  voltage  drops  with  increase  of  cur- 
rent, as  a  constant  current  transformer  or  an  electrostatic 
machine,  etc. 

The  disruptive  voltage  essentially  depends  on  the  gas  pressure 
in  the  space  between  the  electrodes,  and  also  on  the  chemical 
nature,  and  on  the  temperature  of  the  gas.  It  is  over  a  wide 
range,  directly  proportional  to  the  gas  pressure.  Thus,  at  n 
atmospheres  pressure  the  voltage  required  to  jump  a  spark 
between  two  terminals  is  n  times  as  great  as  at  one  atmosphere. 
This  law  seems  to  hold  from  the  highest  pressures  which  have 
been  investigated  down  to  pressures  of  a  few  mm.  mercury,  that 
is,  down  to  about  T^  atmosphere.  When  coming  to  still  lower 
pressures,  however,  the  disruptive  voltage  decreases  less,  ulti- 
mately reaches  a  minimum  —  usually  somewhere  between  1  mm. 
and  0.1  mm.  mercury  pressure  — and  then  increases  again  and 
at  extremely  high  vacua  becomes  much  higher  than  at  atmos- 
pheric pressure,  so  that  it  seems  that  it  is  infinite  in  a  perfect 
vacuum,  that  is,  no  voltage  can  start  conduction  through  a 
perfect  vacuum.  As  the  gas  filling  the  space  is  the  conductor 
in  disruptive  conduction,  it  is  easily  understood  that  in  a  per- 
fectly inert  space,  or  an  absolute  vacuum,  no  disruptive  con- 
duction would  exist. 

The  visible  phenomena  of  disruptive  conduction  very  greatly 
change  with  the  change  of  gas  pressure;  from  the  electrostatic 
spark  at  atmospheric  pressures  to  the  Geissler  tube  glow  in  the 
vacuum;  but  the  change  is  gradual,  thus  showing  the  identity 
of  the  two  phenomena.  At  atmospheric  pressure,  disruptive 
conduction  occurs  by  a  sharply  denned,  relatively  thin  and  noisy 
spark  of  very  high  brilliancy,  which  traverses  the  space  between 
the  electrodes  in  an  erratic  zigzag  path,  not  unlike  in  appearance 
to  the  mechanical  fracture  of  a  solid  material;  and,  indeed,  the 
spark  is  an  electrostatic  rupture  of  the  gas.  If  the  electrostatic 
field  is  fairly  uniform,  as  between  parallel  plates,  or  between 
spheres  of  a  diameter  1.5  or  more  times  their  distance,  with 
gradual  rising  voltage,  the  spark  occurs  when  the  disruptive 
voltage  is  reached,  without  being  preceded,  at  lower  voltage,  by 


LUMINESCENCE.  101 

any  other  phenomenon.  If,  however,  the  electrostatic  field  is 
not  uniform,  as,  for  instance,  between  needle  points  or  small 
spheres  or  wires,  with  increasing  voltage  the  disruptive  strength 
of  the  gas  is  exceeded  at  those  places  where  the  field  intensity  is 
highest,  as  at  the  needle  points,  before  the  disruptive  voltage  of 
the  spark  gap  is  reached,  and  then  a  partial  break  down  occurs 
at  the  points  of  maximum  field  intensity,  as  at  the  needle  points, 
or  at  the  surface  of  high  potential  conductors,  etc.  A  blue  glow, 
then,  appears  at  the  needle  points  followed  by  violet  streamers 
(in  air,  the  color  being  the  nitrogen  spectrum;  in  other  gases 
other  colors  appear),  and  gradually  increases  in  extent  with 
increasing  voltage,  the  so-called  "  brush  discharge,"  or  "  corona." 
Between  needle  points  the  brush  discharges  increase  in  extent, 
and  approach  each  other  until  they  bridge  nearly  60  per  cent  of 
the  gap,  and  then  the  static  spark  occurs. 

At  higher  gas  pressures  the  spark  increases  in  brilliancy,  in 
noisiness,  but  gets  thinner.  If,  however,  we  gradually  decrease 
the  gas  pressure,  the  spark  gets  thicker,  less  brilliant,  and  less 
noisy,  its  edges  are  less  sharply  defined,  that  is,  get  more  diffused, 
and  ultimately  it  passes  between  the  terminals  as  a  moderately 
bright,  thick  and  noiseless  stream,  gradually  fading  at  its  outside, 
and  at  still  higher  vacua  it  fills  the  entire  space  of  the  vacuum 
tube.  At  the  same  time  the  required  voltage  is  decreased  with 
decreasing  gas  pressure,  as  discussed  above. 

46.  I  show  you  here  (Fig.  31)  the  gradual  change  from  the 
static  spark  to  the  Geissler  tube  glow:  in  a  closed  glass  tube  G, 
I  have  two  needle-shaped  terminals,  5  cm.  distant  from  each  other, 
and  supply  them  with  energy  from  a  small  33, 000- volt  trans- 
former. You  see  the  oscillating  static  spark  at  atmospheric 
pressure.  By  now  exhausting  the  tube,  while  the  voltage  is 
maintained  at  the  terminals,  you  can  watch  the  gradual  change 
from  the  static  spark  to  the  Geissler  tube  glow.  In  this  experi- 
ment, a  small  condenser,  a  Leyden  jar,  is  shunted  across  the  high- 
potential  terminals  of  the  transformer,  to  guard  against  the 
disruptive  conduction  changing  to  continuous  conduction,  that 
is,  to  an  arc,  and  a  reactance  inserted  into  the  low-tension  pri- 
mary of  the  step-up  transformer,  to  limit  the  discharge  current, 
as  shown  diagrammatically  in  Fig.  31. 

If  the  Geissler  tube  has  a  considerable  diameter,  3  to  5  cm., 
the  Geissler  discharge  with  alternating  current  is  striated;  that 


102 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


is,  disk-shaped  bright  spots  with  diffused  outlines  alternate  with 
less  luminous  spaces,  about  as  shown  in  Fig.  32.  The  distance 
between  the  luminous  disks  increases  with  decrease  of  the  gas 
pressure.  Two  sets  of  such  disks  exist,  one  issuing  from  the 
one,  the  other  from  the  other  terminal.  They  are  stationary 


FIG.  31. 

only  if  the  gas  pressure  is  perfectly  constant,  but  separate  and 
contract  with  the  slightest  change  of  pressure,  hence  are  almost 
never  at  rest,  but  constantly  moving  through  each  other.  The 
two  sets  of  disks,  by  passing  through  each  other  during  their 
motion,  give  rise  to  a  number  of  different  appearances.  Some 
of  the  successive  shapes  are  shown  in  Fig.  32. 

The  voltage  distribution  in  the  space  between  the  terminals, 
in  disruptive    conduction,   also:  changes  with  the  pressure-  at 


LUMINESCENCE. 


103 


atmospheric  pressure,  practically  all  the  voltage  is  consumed  in 
the  space  between  the  terminals,  and  between  needle  points  for 
distances  of  10  cm.  and  over  very  closely  4000  volts  effective 
alternating  per  cm.  (10,000  volts  per  inch)  are  required  (a  2-cm. 
gap  between  needle  points,  however,  requires  10,000  volts).  With 


II 


II  II 


FIG.  32. 


decreasing  gas  pressure  the  voltage  consumed  in  the  space  be- 
tween the  terminals  decreases,but  the  voltage  consumed  at  the 
terminals  increases,  and  in  a  good  Geissler  tube  vacuum  with 
nitrogen  gas  filling  the  space  between  the  terminals,  from  1000  to 
3000  volts  may  be  consumed  at  the  terminals,  while  the  voltage 
consumed  in  the  space  between  the  terminals  may  drop  as  low 
as  2  volts  per  cm. 

The  voltage  consumed  at  the  terminals  seems  to  decrease  v  ith 
increase  of  their  size.    The  voltage  consumed  in  the  space  be- 


104  RADIATION,  LIGHT,  AND  ILLUMINATION. 

tween  the  terminals,  that  is,  in  the  luminous  stream  of  the  Geiss- 
ler  tube,  seems  to  be  practically  independent,  not  only  of  the 
current,  but  also  of  the  size  of  the  tube,  as  should  be  expected 
with  a  disruptive  discharge.  It  varies,  however,  with  the  tem- 
perature, and  is  different  with  different  gases,  that  is,  different 
gases  have  different  disruptive  strength. 

The  light  given  by  the  Geissler  tube  shows  the  spectrum  of  the 
gas,  and  thus  is  very  bright  and  fairly  efficient  with  a  gas  as  nitro- 
gen, which  gives  a  large  number  of  spectrum  lines  in  the  visible 
range,  and  less  efficient  with  a  gas  as  carbon  dioxide  or  hydrogen, 
in  which  the  lines  in  the  visible  range  represent  only  a  small  part 
of  the  radiated  energy. 

The  industrial  use  of  the  electro-luminescence  of  discontinuous 
conduction,  that  is,  Geissler  tube  lighting,  is  still  very  limited 
(Moore  tube).  So  far  only  nitrogen  gives  a  fairly  good  efficiency, 
reaches  apparently  values  between  the  tungsten  lamp  and  the 
tantalum  lamp ;  or,  a  specific  consumption  of  two  watts  per  mean 
spherical  candle  power.  The  color  of  the  nitrogen  spectrum  is 
a  golden  yellow.  As  the  range  of  gas  pressure  in  which  the 
voltage  is  near  the  minimum  is  very  narrow,  and  the  gas  pres- 
sure changes  during  operation,  by  absorption  at  the  electrodes, 
etc.,  means  have  to  be  provided  to  maintain  constant  gas  pressure 
by  automatically  feeding  gas  into  the  tube  whenever  the  pres- 
sure drops  below  the  minimum  voltage  or  maximum  efficiency 
point.  The  greatest  disadvantage  of  Geissler  tube  lighting, 
however,  is  the  high  voltage  required  at  the  terminals.  To  get 
fair  efficiency  the  tube  must  be  so  long  that  the  voltage  con- 
sumed in  the  stream  —  which  represents  the  power  converted 
into  light  — is  much  larger  than  the  voltage  consumed  at  the 
terminals  — which  represents  wasted  power.  With  a  terminal 
drop  of  2000  volts,  and  two  volts  per  cm.  in  the  conducting  gas 
stream,  to  use  half  of  the  supply  voltage  for  light  production,  thus 

2000 
requires  a  tube  length  of  — — -  =  1000  cm.  =  10  m.  or  33  feet, 

2 

and  to  use  80  per  cent  of  the  supply  voltage  for  light  production, 
that  is,  waste  only  20  per  cent  of  the  supplied  power  in  heating 

onrvrj 

the  terminals,  requires  a  tube  length  of  — —  =  40  m.  or  133  feet. 

<L 

Thus  the  Geissler  tube  as  an  illuminant  is  essentially  a  large  unit 


LUMINESCENCE.  105 

of  light,  requiring  high  voltage  (which  obviously  may  be  produced 
by  a  transformer  at  the  tube)  and  having  a  very  great  size.  It 
gives,  however,  low  intrinsic  brilliancy  and  splendid  diffusion  of 
the  light. 

Continuous  Conduction. 

47.  In  continuous  conduction,  or  arc  conduction,  the  conductor 
is  a  stream  of  electrode  vapor,  which  bridges  the  gap  between  the 
electrodes  or  terminals. 

While  in  the  spark,  or  the  Geissler  discharge,  the  conductor  is 
the  gas  which  fills  the  space  between  the  terminals,  in  the  electric 
arc  the  current  makes  its  own  conductor,  by  evaporation  of  the 
electrode  material,  and  maintains  this  conductor  by  maintain- 
ing a  supply  of  conducting  vapor.  The  color  and  the  spectrum 
of  the  arc,  thus,  are  those  of  the  electrode  material,  and  not  of 
the  gas  which  fills  the  space  in  which  the  arc  is  produced,  and 
the  nature  of  the  gas  in  the  space  thus  has  no  direct  effect  on 
the  arc.  Its  pressure  obviously  has  an  effect,  as  the  vapor  pres- 
sure of  the  conducting  arc  stream  is  that  of  surrounding  space, 
thus  increases  with  increasing  gas  pressure,  and  the  arc  vapor 
then  contracts,  the  arc  gets  thinner,  while  with  decrease  of  the 
gas  pressure  in  the  space  surrounding  the  arc  the  vapor  pressure 
of  the  arc  stream  also  decreases,  thus  the  vapor  expands,  and 
the  arc  stream  becomes  larger  in  section  and  correspondingly 
less  luminous. 

As  the  arc  conductor  is  a  vapor  stream  of  electrode  material, 
this  vapor  stream  must  first  be  produced,  that  is,  energy  must 
first  be  expended  before  arc  conduction  can  take  place.  An  arc, 
that  is,  continuous  conduction,  therefore,  does  not  start  spon- 
taneously between  the  arc  terminals  if  sufficient  voltage  is  sup- 
plied at  the  terminals  to  maintain  the  arc,  but  the  arc  has  first 
to  be  started,  that  is,  the  conducting  vapor  bridge  produced  by 
the  expenditure  of  energy. 

If,  therefore,  in  the  arc  the  current  ceases  even  momentarily, 
the  conduction  ceases  by  the  disappearance  of  the  vapor  stream 
and  does  not  start  again  spontaneously,  but  the  arc  has  to  be 
started  by  producing  a  vapor  stream.  With  alternating  voltage 
supply  the  arc,  thus,  would  go  out  at  the  zero  of  current  and  have 
to  be  started  again  at  every  half  wave.  In  general,  the  arc,  thus, 
is  a  direct  current  phenomenon. 


106  RADIATION,  LIGHT,  AND  ILLUMINATION. 

Some  of  the  means  of  starting  arc  conduction  are : 

(1.)  By  bringing  the  terminals  into  contact  with  each  other 
and  thereby  closing  the  circuit,  that  is,  establishing  the  current, 
and  then  slowly  separating  them.  In  the  moment  of  separation 
the  contact  point  is  heated,  vapor  produced  at  it,  and  during  the 
separation  of  the  terminals,  a  vapor  stream  is  left  behind  as 
conducting  bridge.  Obviously,  if  the  terminals  are  separated 
very  rapidly,  and  the  voltage  is  not  much  higher  than  required 
to  maintain  the  arc,  not  enough  vapor  may  be  produced  to  con- 
duct the  current,  and  the  arc  does  not  start. 

(2.)  By  raising  the  voltage  between  the  terminals  so  high  that 
a  static  spark  passes  between  them,  that  is,  disruptive  conduction 
occurs.  The  energy  of  this  static  spark,  if  sufficiently  large,  that 
is,  if  the  high  voltage  is  maintained  sufficiently  long,  then  pro- 
duces the  vapor  stream  and  starts  the  arc,  that  is,  the  arc  follows 
the  spark.  If  the  duration  of  the  high  voltage  is  very  short,  the 
energy  of  the  spark  may  not  be  sufficient  to  start  the  arc.  Thus 
high  frequency  discharges  between  live  terminals  frequently  are 
not  followed  by  an  arc,  and  the  lower  the  voltage  between  the 
terminals  is,  the  more  powerful  a  static  spark  is  required  to  start 
an  arc. 

(3.)  By  supplying  the  conducting  vapor  stream  from  another 
arc,  that  is,  by  an  auxiliary  arc.  If  the  vapor  stream  of  this 
auxiliary  arc  issues  from  the  same  terminal  as  the  vapor  stream 
of  the  main  arc  which  is  to  be  started,  only  the  normal  operating 
voltage  is  required  in  starting  the  latter  arc,  while  a  higher  volt- 
age is  required,  if  the  vapor  is  supplied  by  an  entirely  separate 
arc. 

(4.)  By  raising  the  space  between  the  terminals  to  a  very  high 
temperature,  as  by  bridging  the  terminals  by  a  carbon  filament, 
and  by  the  passage  of  current  raising  this  filament  to  very  high 
temperature. 

48.  The  sharp  distinction  between  the  arc,  in  which  the  cur- 
rent makes  its  own  conductor  by  a  vapor  stream  issuing  from 
the  terminals,  and  the  Geissler  discharge,  in  which  the  current 
uses  the  gas  which  fills  the  space  as  conductor,  is  best  illustrated 
by  using  in  either  case  the  same  material,  mercury,  as  conductor. 
I  have  here  a  vacuum  tube,  shown  to  scale  in  Fig.  33,  about  25. 
cm.  diameter,  with  three  mercurv  terminals.  The  tube  has  four 
mercury  terminals,  of  which,  however,  I  use  only  three.  The 


LUMINESCENCE. 


107 


gas  which  fills  the  space  between  the  terminals  is  mercury  vapor. 

1  now  connect,  as  shown  diagrammatically  in  Fig.  34,  terminals 

2  and  3  to  the  high  potential  coil  of  a  step-up  transformer  —  the 
low  potential  circuit  contains  a  reactance  to  limit  the  current  - 
and  you  see  the  striated  Geissler  discharge  through  mercury 


FIG.  33. 

vapor  appear  between  terminals  2  and  3,  giving  the  green  light> 
of  the  mercury  spectrum.  The  terminals  are  quiet,  as  they  do 
not  participate  in  the  conduction.  I  now  connect  terminals  1 
and  2  through  a  resistance,  to 'a  direct  current  supply,  and  tilt 
the  tube  momentarily  to  let  some  mercury  run  over  from  2  to  1, 
and  by  thus  momentarily  connecting  these  terminals,  establish 
the  current  and  so  start  the  arc,  and  you  see  the  mercury  arc 
pass  between  terminals  1  and  2,  and  see  at  one  terminal  —  the 
negative  one  —  a  rapidly  moving  bright  spot,  which  marks  the 
point  from  which  the  vapor  stream  issues  which  carries  the  cur- 
rent. We  have  here  in  one  and  the  same  vacuum  tube,  and 
with  the  same  material  —  thus,  the  same  color  and  spectrum  of 
light,  both  types  of  conduction  —  the  continuous  high  current  and 
low  voltage  conduction  of  the  mercury  arc,  and  the  striated  high 
voltage  low  current  disruptive  conduction  of  the  Geissler  dis- 
charge through  mercury  vapor. 

The  conducting  vapor  stream  which  carries  the  current  in  the 
arc,  at  least  in  all  arcs  which  so  far  have  been  investigated,  issues 


108 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


from  the  negative  terminal  or  cathode,  and  is  in  rapid  motion 
from  the  negative  towards  the  positive.  The  character  of  the 
arc,  therefore,  is  determined  by  the  material  of  the  negative 
terminal,  the  temperature  of  the  arc  stream  in  general  probably 
is  the  temperature  of  the  boiling  point  of  the  negative  terminal, 


3J=10  OHMS 


FIG.  34. 

and  the  spectrum  of  the  arc  is  the  spectrum  of  the  negative  ter- 
minal. An  exception  herefrom,  occurs  only  in  those  cases  in 
which  the  positive  terminal  contains  material  which  boils  below 
the  temperature  of  the  arc  stream  (flame  carbons)  and  the  posi- 
tive terminal  is  made  so  small  that  its  tip  is  raised  to  the 
temperature  of  the  arc  stream,  and  at  this  temperature  heat 
evaporation  of  the  material  of  the  positive  occurs.  These  vapors 
enter  the  arc  stream,  and  there  become  luminous,  possibly  by 
chemical  luminescence,  and  add  their  spectrum  to  that  of  the  arc 
conductor,  that  is,  the  negative  material.  In  this  case  the  arc 
spectrum  shows  the  negative  as  well  as  the  positive  material,  or 
at  least  the  more  volatile  components  of  the  positive  material. 


LUMINESCENCE.  109 

With  the  exception  of  this  case  of  heat  evaporation  from  the 
positive  terminal,  the  material  of  the  positive  terminal  does  not 
participate  in  the  phenomena  occurring  in  the  arc.  Thus  the 
positive  can  be  made  of  any  conducting  and  refractory  material, 
and  if  made  sufficiently  large  not  to  get  too  hot,  does  not  con- 
sume; only  the  negative  terminal  of  the  arc  consumes  in  feeding 
the  arc  flame,  that  is,  supplying  the  vapor  conductor,  but  the 
positive  is  inherently  non-consuming,  and  may  be  made  a  perma- 
nent part  of  the  arc-lamp  mechanism.  On  the  contrary,  if  the 
positive  is  made  so  large  that  its  temperature  remains  very  much 
below  the  arc  temperature,  condensation  of  the  arc  vapor  occurs 
at  it,  and  it  builds  up,  that  is,  increases  in  size.  Consumption 
of  the  positive  terminal  is  thus  due  merely  to  the  heat  produced 
at  it  by  combustion  or  heat  evaporation. 

While  the  arc  conductor  issues  from  the  negative  terminal,  in 
general  more  heat  is  produced  at  the  positive  terminal.  Thus 
with  both  terminals  of  the  same  size  and  material,  as  usual  in 
the  carbon  arc,  the  positive  gets  hotter,  and  therefore  in  open 
air  burns  off  faster,  which  has  led  to  the  erroneous  assumption 
that  the  positive  feeds  the  arc. 

While  carbon  is  the  material  most  commonly  used  as  termi- 
nals, the  carbon  arc  is  not  a  typical  arc,  but  is  an  exceptional  arc. 

(1)  Because  carbon  is  one  of  the  very  few  substances  which 
change  directly  from  the  solid  to  the  vapor  state,  that  is,  do  not 
melt  at  atmospheric  pressure,  but  boil  below  the  melting  point. 

(2)  Carbon  is  the  most  refractory  substance  and  the  tempera- 
ture of  the  carbon  arc  higher  than  the  boiling  point  of  any  other 
substance.    Any  material  existing  in  the  terminals  of  a  carbon 
arc  thus  evaporates,  and  by  entering  the  arc  stream  shows  its 
spectrum,  so  that  luminescent  material  can  be  fed  into  the  carbon 
arc  from  either  terminal. 

(3)  At  the  temperature  of  the  carbon  arc  all  gases  and  vapors 
have  become  good  conductors,  and  a  carbon  arc  thus  can  operate 
equally  well  on  alternating  current  as  on  direct  current;  that  is, 
the  voltage  required  to  maintain  the  carbon  arc  is.  sufficient, 
after  the  reversal  of  current,  to  restart  it  through  the  hot  carbon 
vapor. 

A  typical  arc  is  shown  in  Fig.  35  as  the  magnetite  arc, 
with  a  lower  negative  terminal  M  consisting  of  magnetite, 
the  non-consuming  upper  terminal  C  of  copper,  and  of  such 


110 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


size  that  it  does  not  get  so  hot  as  to  oxidize  or  evaporate, 
but  sufficiently  hot  to  avoid  condensation  of  magnetite  vapor 
on  it. 

The  arc  flame  consists  of  an  inner  cylindrical  core  A,  of  bluish 
white  color  and  high  brilliancy,  slightly  tapering  at  both  ends, 
which  is  surrounded  by  a  less  luminous  shell  B,  of  more  yellowish 
color,  narrowest  at  the  negative  end,  and  increasing 
in  diameter  towards   the   positive,  surrounding  the 
latter. 

The  inner  core  A  is  the  arc  conductor,  or  con- 
ducting vapor  stream,  while  the  outer  shell  B  is 
non-conducting  luminous  vapor,  possibly  containing 
particles  of  solid  material  floating  in  it  as  incan- 
descent bodies. 

The  arc  conductor  A  issues  from  a  depression  S  in 
a  melted  pool  P  formed  on  the  surface  of  the  terminal 
M.  This  depression  S  is  in  a  rapid  and  erratic 
motion,  and  thereby  causes  a  constant  and  rapid 
flickering  of  the  arc.  It  is  this  flickering,  inherent  to 
all  arcs  in  which  the  negative  terminal  is  fusible  (which 
therefore  does  not  exist  in  the  carbon  arc),  which  has 
retarded  the  industrial  development  of  the  more  efficient  metal 
arcs  until  late  years.  Its  cause  is  the  reaction  exerted  by 
the  velocity  of  the  vapor  blast  from  the  negative,  which  presses 
the  surface  of  the  liquid  pool  down  at  the  point  from  which 
the  current  issues.  The  starting  point  of  the  current  con- 
tinuously climbs  up  the  side  of  this  depression,  in  shortening 
the  arc,  but,  in  doing  so,  depresses  its  new  starting  point, 
that  is,  the  depression  S,  and  thereby  the  negative  end  of  the 
arc  stream  moves  over  the  surface  the  faster  the  more  fluid 
the  surface  is.  In  the  mercury  arc,  this  phenomenon  of  the 
running  spot  at  the  negative  terminal  is  also  very  marked,  but 
not  so  objectionable,  as  the  arc  stream  is  so  long  that  the  flicker 
at  the  negative  terminal  has  no  effect  on  the  total  light.  This 
flickering  disappears  in  the  magnetite  arc  if  we  destroy  the 
fluidity  of  the  melted  magnetite  by  mixing  with  it  some  much 
more  refractory  material,  as  chromite.  The  chromite  remains 
solid  and  holds  the  melted  magnetite  like  a  sponge.  The  reaction 
of  the  vapor  blast,  then,  cannot  depress  its  starting  point,  and  no 
tendency  exists  of  shifting  the  starting  point,  and  the  arc  becomes 


FIG.  35. 


LUMINESCENCE. 


Ill 


steady.     In  this  manner  such  arcs  have  now  been  made  steady 
and  thereby  suitable  for  industrial  use. 

49.  Since  the  arc  conduction  issues  as  a  rapidly  moving  vapor 
stream  from  the  negative  terminal  or  cathode,  it  must  be  con- 
tinuous at  the  cathode;  if  interrupted  even  for  a  very  short  time 
at  the  cathode,  a  break  exists  in  the  continuity  of  the  conductor 
and  conduction  ceases,  that  is,  the  arc  extinguishes.  At  any 
other  point  of  the  arc  stream,  however,  a  break  in  the  continuity 
of  the  stream  may  exist,  provided  that  current  continues  from 
the  negative,  since  such  a  break  in  the  continuity  of  the  con- 
ducting vapor  stream  is  bridged  again,  and  conduction  re-estab- 
lished by  the  vapor  stream  coming  from  the  negative.  Thus  the 


FIG.  36. 

arc  can  be  started  by  merely  starting  a  conducting  vapor  stream 
from  the  negative,  as  by  an  auxiliary  arc.  As  soon  as  this  con- 
ducting vapor  reaches  the  positive  terminal,  it  closes  the  circuit 
and  establishes  conduction.  An  arc  can  be  shifted  or  jumped 
from  one  positive  terminal  to  another  one,  but  cannot  be  shifted 
from  negative  to  negative;  the  negative  terminal,  as  the  source 
of  the  conducting  vapor  stream,  must  be  continuous. 

To  illustrate  this,  I  have  here  (Fig.  36)  in  a  hand  lamp  two 
copper  rods  A  and  B  of  about  5  mm.  diameter,  as  arc  terminals, 
separated  by  2.5  cm.,  and  connected  into  a  220- volt  direct-cur- 
rent circuit,  with  sufficient  resistances  in  series  to  limit  the  current 
to  about  4  amperes.  A  third  copper  rod  of  the  same  size,  C, 
is  connected  by  a  flexible  lea.J  to  the  upper  terminal  B.  I  close 
the  reversing  switch  S  so  as  to  make  A  negative,  and  B  and  O 

,  .  '..  i          \.      ,   :   ;    ,-    ,.    .    - 


112  RADIATION,  LIGHT,  AND  ILLUMINATION. 

positive,  and  start  an  arc  between  A  and  C  by  touching  C  to  A. 
I  draw  this  arc  to  about  4  cm.  length,  and  without  touching  C 
with  B,  as  soon  as  the  conducting  vapor  stream  of  the  arc  AC 
(the  inner  core  A  of  Fig.  35)  touches  B,  as  shown  in  Fig.  36,  the 
arc  leaves  C  and  goes  to  B,  that  is,  by  the  arc  AC  I  have  started 
arc  AB.  If  I  had  separate  resistances  in  series  with  the  terminals 
B  and  (7,  the  arc  AC  would  also  continue  to  exist  after  it  started 
arc  AB-  otherwise,  as  two  arcs  cannot  run  in  parallel,  the  longer 
arc,  AC,  goes  out  as  soon  as  the  shorter  arc  AB  starts. 

I  now  reverse  the  circuit  by  throwing  switch  S,  and  make  A 
positive,  and  B  and  C  negative,  again  start  AC  by  contact,  and 
draw  it  out  until  the  arc  flame  wraps  itself  all  around  terminal 


FIG.  37. 

B}  but  the  arc  does  not  transfer.  I  even  insert  10  ohms  resist- 
ance rl  in  series  with  C  (Fig.  37),  so  that  the  voltage  AB  is  about 
40  volts  higher  than  AC,  that  is,  B  by  40  volts  more  negative 
than  C,  and  still  the  arc  does  not  transfer.  I  now  touch  C  with 
B  and  separate  it  again;  if  during  contact  the  negative  spot 
during  its  motion  happens  to  run  over  to  terminal  B,  the  arc  con- 
tinues between  B  and  A;  if,  however,  the  negative  spot  has 
remained  on  C,  when  separating  again,  the  arc  remains  at  C  as 
negative,  although  B  is  more  negative  by  40  volts. 

An  arc  therefore  can  be  started  at  its  normal  starting  voltage 
by  an  auxiliary  arc  having  the  same  negative,  but  not  by  an 
auxiliary  arc  with  the  same  positive,  and  an  arc  can  be  shifted 
from  one  positive  to  another,  but  not  from  one  negative  to 


LUMINESCENCE. 


113 


another.  The  cause  is,  as  explained  above,  the  necessity  of  the 
continuity  at  the  negative  terminal  as  the  source  of  the  conduct- 
ing vapor  stream. 

Still  more  startling  is  the  following  demonstration :  I  shift  the 
resistance  rl  from  C  to  B,  and  start  the  arc  from  A  to  B,  with  B 
as  negative,  by  bringing  these  terminals  into  contact  with  each 
other,  and  then  separating  them.  The  auxiliary  terminal  C 
(Fig.  38)  now  is  by  40  volts  more  negative  than  the  negative 
terminal  B  of  the  arc.  I  now  cut  slowly  through  the  arc  stream 
by  moving  C  across  it  between  A  and  B,  as  shown  in  Fig.  38: 
the  arc  AB  remains,  but  no  current  goes  to  C,  although  more 


r  =20  OHMS 

ws 


FIG.  38. 

negative,  that  is,  at  a  higher  potential  difference  and  a  shorter 
distance  against  A  than  B  is.  I  even  hold  C  for  some  time  in 
the  conducting  core  of  the  arc  AB,  and  still  the  current  does  not 
shift  from  the  negative  B  to  the  still  more  negative  terminal  C. 
This  experiment  is  interesting  in  demonstrating  that  a  conductor 
immersed  into  the  arc  flame  does  not  assume  the  potential  of  the 
arc  flame,  but  may  differ  therefrom  by  considerable  voltage,  and 
that  it  therefore  is  not  feasible  to  determine  the  potential  dis- 
tribution in  an  arc  by  means  of  exploring  electrodes,  as  has 
frequently  been  attempted. 

Obviously,  if  I  now  reverse  the  circuit,  and  make  B  and  C 
positive,  A  negative,  the  current  leaves  B  and  goes  to  C  as  soon 
as  C  touches  the  conducting  core  of  the  arc  AB. 

50.  The  electric  arc,  therefore,  is  a  unidirectional  conductor, 
that  is,  the  vapor  stream  is  conducting  between  its  negative 


114 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


terminal  A  in  Fig.  36,  that  is,  the  starting  point  of  the  arc 
stream,  and  any  point  reached  by  it  which  is  positive  to  A,  but 
is  non-conducting  for  any  point  which  is  negative  with  respect 
to  A. 

If,  now,  in  Fig.  38,  with  the  terminal  C  immersed  in  the  arc 
stream,  I  connect  A  and  C  to  a  source  of  alternating  voltage, 
as  shown  in  Fig.  39,  while  a  direct-current  arc  flows  from  A  to  B, 
with  A  as  negative,  then  during  that  half-wave  of  the  alternating 
voltage,  for  which  C  is  positive  to  A,  there  is  current  between  A 
and  (7,  while  for  the  reverse  half-wave,  in  which  C  is  negative  to 
A,  there  is  no  current.  The  arc  thus  rectifies  the  alternating 
voltage,  and  the  rectification  is  complete,  that  is,  there  is 


T=  30  OHMS 

MAA 


FIG.  39. 

current  during  one  half-wave  only,  but  no  current  at  all  dur- 
ing .the  other.  I  show  you  this  experimentally,  using  50  volts 
alternating  between  A  and  (7.  With  this  arrangement,  to 
maintain  the  rectification  continuously,  obviously  the  ter- 
minal C  would  have  to  be  cooled. 

Alternating  voltage  thus  can  be  rectified  by  means  .of  the 
unidirectional  character  of  the  arc :  if  a  continuous  vapor  stream 
is  maintained  from  one  terminal,  either  by  direct-current  ex- 
citation or  by  overlapping  several  waves  of  alternating  cur- 
rent, current  is  in  that  direction  only  in  which  this  exciter 
terminal  is  negative,  but  not  in  the  opposite  direction. 

.  Such  arc  rectifiers  —  of  which  the  mercury  arc  rectifier  is  the 
most  commonly  used  — have  been  developed  and  extensively 
introduced  in  the  industry,  of  la.te  years,  for  operating,  low-volt- 


LUMINESCENCE. 


115 


age  constant  direct  potential  and  high-voltage  constant  direct- 
current  circuits  from  a  source  of  alternating  voltage.  Regarding 
the  electrical  phenomena  occurring  in  arc  rectification,  see 
"  Theory  and  Calculation  of  Transient  Electric  Phenomena  and 
Oscillations/'  Section  II,  Chapter  IV. 

The  inability  of  an  alternating  voltage  to  maintain  an  arc, 
I  show  you  here  on  the  same  apparatus  by  connecting  the  two 
terminals  (Fig.  40)  A  and  B  to  the  1000-volt  terminals  of  a 
transformer  —  with  sufficient  resistance  in  series  to  limit  the 
current. 

While  220  volts  direct  current  easily  maintained  a  steady 
2-cm.  arc  between  these  terminals,  with  1000  volts  alternating 
between  the  terminals,  if  I  try  to  produce  an  alternating  arc 
by  gradually  separating  the  terminals,  the  circuit  opens  before 
the  terminals  have  separated  1  mm.;  that  is,  1000  volts  alter- 
nating cannot  maintain  an  arc  of  1  mm.  between  these  copper 

Fh 


i  =  iu  unM5 

v— W 


110  VJOLTS 
60  CYCLES 


FIG.  40. 


terminals.  The  cause  is  obvious:  to  maintain  an  arc  between 
two  terminals,  a  voltage  is  required  sufficiently  high  to  restart 
the  arc  at  every  half-wave  by  jumping  an  electrostatic  spark 
between  the  terminals  through  the  hot  residual  vapor  of  the 
preceding  half-wave.  The  voltage  required  by  an  electro- 
static spark,  that  is,  by  disruptive  conduction,  decreases  with 
increase  of  temperature:  for  a  13-mm.  (0.5-in.)  gap,  it  is  about 
10,000  volts  at  atmospheric  temperature,  7000  volts  at  the 
boiling  point  of  mercury  (360  deg.  cent.),  2500  volts  at  the 
boiling  point  of  zinc  (1000  deg.  cent.),  500  volts  at  the  boiling 
point  of  magnetite  (2000  deg.  cent.),  100  volts  at  the  boiling 
point  of  titanium  carbide  (3000  deg.  cent.),  40  volts  at  the 
boiling  point  of  carbon  (3500  deg.  cent.).  The  voltage  re- 
quired to  maintain  a  13-mm.  alternating  arc  must  therefore  be 


116 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


Sit  least  as  high  as  given  by  a  curve  somewhat  like  curve  I  in 
Fig.  41  *  (to  bring  the  values  of  voltage  within  the  scale  of  the 
figure,  the  logarithm  of  voltage,  as  ordinate,  is  plotted  against 
the  temperature  as  abscissa). 

The  voltage  required  to  maintain  an  arc,  that  is,  the  direct- 
current  arc  voltage,  increases  with  increasing  arc  temperature, 
and  thereby  increasing  radiation,  etc.  For  a  13-mm.  (0.5-in.) 


FIG.  41. 


arc  it  is  approximately  shown  as  Curve  II  in  Fig.  41 :  20  volts 
for  the  mercury  arc,  40  volts  for  the  zinc  arc,  60  volts  for  the 

*  As  the  disruptive  voltage  also  depends  on  the  chemical  nature  of  the 
vapor,  that  is,  some  gases  and  vapors  have  a  higher  disruptive  strength  than 
others,  as  discussed  above,  the  arrangement  of  the  different  materials  regard- 
ing their  alternating  arc  voltages  is  not  entirely  determined  by  their  boiling 
points,  but  modified  by  individual  characteristics.  It  further  depends  on  the 
current:  at  higher  currents  and  thus  larger  amounts  of  residual  vapor,  the 
voltage  is  lower.  It  further  depends  on  the  frequency:  the  lower  the  fre- 
quency and  the  greater,  therefore,  the  cooling  effect  during  the  reversal  of 
current  the  higher  is  the  required  voltage. 


LUMINESCENCE.  117 

magnetite  arc,  75  volts  for  the  titanium  carbide  arc,  80  volts 
for  the  carbon  arc.* 

As  seen  from  Fig.  41,  the  curves  I  and  II  intersect  at  some 
very  high  temperature,  near  the  boiling  point  of  carbon,  and 
materials  which  have  a  boiling  point  above  the  temperature  of 
intersection  of  these  curves  require  a  lower  voltage  for  restart- 
ing the  arc  than  for  maintaining  it,  and  a  voltage  sufficient  to 
maintain  the  arc  restarts  it  at  every  half-wave  of  alternating 
current,  that  is,  such  materials  can  maintain  a  steady  alternat- 
ing arc  at  the  same  voltage  as  a  direct-current  arc.  Even 
materials  like  titanium  carbide,  in  which  the  starting  voltage  is 
not  much  above  the  running  voltage,  maintain  a  steady  alter- 
nating arc,  as  in  starting,  the  voltage  consumed  during  running 
in  the  steadying  resistance  or  reactance  is  available. 

Alternating  arcs  thus  can  be  maintained  at  moderate  volt- 
ages only  by  a  few  materials  of  extremely  high  boiling  points,  as 
carbon  and  carbides,  but  by  far  the  largest  number  of  materials 
cannot  be  used  as  terminals  of  an  alternating-current  arc. 

In  Fig.  41  the  range  between  the  curves  I  and  II  is  the 
"  rectify  ing  range,"  as  in  this  range  unidirectional  current  is 
produced  from  an  alternating  source  of  voltage  through  the  arc, 
if  the  arc  conductor  is  maintained  by  excitation  of  its  negative 
terminal.  The  voltage  range  of  rectification  thus  is  highest  in 
the  mercury  arc,  which  has  the  lowest  temperature,  and  vanishes 
in  very  high-temperature  arcs.  The  carbon  arc  thus  cannot 
give  complete  rectification,  while  the  mercury  arc,  or  zinc  arc, 
etc.,  can  do  so.  The  mercury  arc,  having  the  greatest  recti- 
fication range,  thus  is  practically  always  used  for  this  purpose. 

Below  curve  II  of  Fig.  41  no  conduction  occurs,  between 
curves  I  and  II,  unidirectional  conduction  takes  place,  and 
above  curve  I,  disruptive  conduction  and  alternating  current 
can  exist. 

51.  The  light,  and  in  general  the  radiation  given  by  the  arc 
proper,  that  is,  by  the  vapor  conductor  which  carries  the  cur- 
rent between  the  terminals,  is  due  to  luminescence,  that  is,  to 
a  more  or  less  direct  transformation  of  electric  energy  into 

*  This  voltage  also  is  not  merely  a  function  of  the  arc  temperature,  but 
modified  somewhat  by  the  chemical  individuality  of  the  material.  It  is  a 
function  of  the  current  and  decreases  with  increase  of  current,  so  that  above 
values  are  approximate  only,  corresponding  to  about  4  amperes. 


118  RADIATION,  LIGHT,   AND  ILLUMINATION. 

radiation,  without  heat  as  intermediary  form  of  energy.  The 
quality  or  color  of  the  light,  or  its  spectrum,  that  is,  the  fre- 
quency or  frequencies  of  radiation  given  by  the  arc  stream, 
thus  are  not  a  function  of  the  temperature,  as  in  the  radiation 
produced  by  heat  energy,  but  the  frequencies  are  those  at 
which  the  luminescent  body  is  capable  of  vibrating,  that  is, 
are  determined  by  the  chemical  nature  of  the  luminescent  body 
or  vapor  conductor.  The  efficiency  of  light  production  thus 
does  not  directly  depend  upon  the  temperature,  does  not  in- 
crease with  increase  of  temperature,  as  in  temperature  radia- 
tion, but  to  some  extent  rather  the  reverse.  We  have  the  same 
relation  as  in  other  energy  transformations:  when  converting 
heat  into  other  forms  of  energy,  the  more  intense  the  heat, 
that  is,  the  higher  the  temperature,  the  higher  efficiency  we 
may  expect.  When  transforming,  however,  some  form  of 
energy  differing  from  heat,  into  another  form  of  energy,  as 
mechanical  into  electrical  energy,  the  heat  produced  repre- 
sents a  waste  of  energy,  and  the  lower  the  temperature,  the 
higher  in  general,  other  things  being  equal,  would  be  the  effi- 
ciency. The  efficiency  of  light  production  by  the  arc  thus  is 
not  a  function  of  the  temperature,  but  the  lowest  temperature 
arc,  the  mercury  arc,  is  one  of  the  most  efficient. 

The  light  given  by  the  arc  contains  only  a  finite  number  of 
definite  wave  lengths,  that  is,  gives  a  line  spectrum:  very  few 
lines  in  the  ordinary  mercury  arc,  many  thousands  in  the  tita- 
nium arc.  The  color  of  the  light  is  essentially  characteristic  of 
the  nature  of  the  luminescent  body.  For  instance,  it  is  white 
in  the  titanium  arc,  as  the  lines  of  the  titanium  spectrum  are 
fairly  uniformly  distributed  over  the  entire  visible  range.  The 
light  of  the  calcium  arc  is  orange  yellow,  as  the  spectrum  lines  of 
calcium  are  more  frequent  and  more  intense  in  the  orange- 
yellow  range  of  radiation,  etc. 

Frequently  a  change  of  the  color  of  the  luminescent  light  of 
the  arc  occurs  with  the  temperature,  but  it  does  not  follow 
a  definite  law,  as  in  temperature  radiation,  but  is  a  char- 
acteristic particularity  of  the  luminescent  body:  some  of  the 
spectrum  lines  increase  more  rapidly  in  intensity,  with  increas- 
ing temperature,  than  others,  and  the  resultant  color  of  the 
light  changes  thereby.  For  instance,  the  ordinary  iron  arc,  as 
produced  by  4  amperes  direct  current  across  a  gap  of  2  cm. 


LUMINESCENCE.  119 

between  iron  or  magnetite  terminals,  and  requiring  about  75 
volts,  is  white  and  very  brilliant,  that  is,  has  a  spectrum  with 
many  lines  about  uniformly  distributed  over  the  visible  range. 
We  can  greatly  increase  the  temperature  of  the  arc  by  using  a 
high-frequency  condenser  discharge:  in  this  case  very  large 
currents  of  very  short  duration  exist  as  oscillations  between  the 
terminals,  with  periods  of  rest  between  the  oscillations,  very 
long  compared  with  the  duration  of  the  current.  In  this  case 
the  duration  of  the  current  is  too  short  to  feed  a  large  volume 
of  electrode  vapor  into  the  arc  stream,  and  as  the  current  is 
very  large  during  the  short  moment  of  the  discharge,  the 
vapor  between  the  terminals  is  very  greatly  overheated.  Oscil- 
lating condenser  discharges  thus  offer  a  means  of  increasing  the 
temperature  of  the  arc  stream  very  greatly  beyond  the  boiling 
point  of  the  material.  When  using  a  condenser  discharge  be- 
tween iron  terminals,  we  thus  get  an  iron  arc  of  very  much 
higher  temperature,  and  this  arc  gives  very  little  visible  light, 
but  a  very  large  amount  of  ultra-violet  radiation.  It  is  this 
arrangement  which  we  have  used  in  the  preceding  to  produce 
ultra-violet  light  by  the  so-called  " ultra-violet  iron  arc."  In 
the  iron  arc  the  average  wave  length  of  the  radiation  thus  shifts 
with  increasing  temperature  to  shorter  wave  lengths,  or  higher 
frequencies,  similar  as  in  temperature  radiation. 

The  reverse  is  the  case  with  the  mercury  arc:  the  ordinary 
mercury  arc  in  an  evacuated  glass  tube,  with  ample  condensing 
chamber,  gives  practically  no  red  light;  only  a  very  powerful 
spectroscope  can  discover  some  very  faint  red  lines.  If  now 
the  condensation  of  the  mercury  vapor  is  made  insufficient, 
by  obstructing  ventilation,  or  greatly  raising  the  current,  or 
omitting  the  condensing  chamber  in  the  construction  of  the 
lamp,  and  the  mercury  vapor  pressure  and  thereby  the  tem- 
perature increased,  at  least  three  red  lines  located  about  as 
shown  in  Fig.  42  become  visible  in  the  mercury  spectrum  even 
in  a  low-power  spectroscope, 


Ill     Oi    i\J  W      IJ\J  W  Cl       Ok-'CLiLlWO^V^lJC, 

and  increase  in  intensity  with  _J [ I 

m  v. ^        ,/    YELLOW     <^^-^_ ^  BLUE  VlO 

increasing  vapor  pressure.  To 


show  you  this  I  use  a  U-shaped  FlG-  42- 

mercury  lamp  constructed  as  shown  half  size  in  Fig.  43.  I  con- 
nect the  lamp  into  a  220-volt  direct-current  circuit,  with  an 
inductive  resistance  in  series  thereto,  to  limit  the  current,  and 


120 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


start  the  arc  by  pouring  some  mercury  over  from  one  side  to 
the  other.  Immediately  after  starting  the  lamp  you  see  no  red 
lines  in  the  low-power  spectroscope  which  I  have  here.  As  with 
the  large  current  which  I  use  —  3  amperes  —  the  mercury  vapor 
cannot  freely  condense,  the  mercury  vapor  pressure  rises  and 


FIG.  43. 

presses  the  mercury  level  down  in  the  center  tubes,  up  in 
the  outside  tubes,  as  indicated  at  b  in  Fig.  43,  and  thereby 
enables  us  to  measure  the  mercury  pressure.  Gradually  you 
see  the  three  red  lines  appear,  and  increase  in  intensity,  and 
when  the  vapor  pressure  has  risen  to  about  5  cm.,  the  three 
red  lines  are  fairly  bright,  and  numerous  other  red  and  orange 
mercury  lines  have  appeared.  At  this  pressure  we  are  so  close 
to  the  softening  point  of  the  glass  that  we  cannot  go  further, 
but  by  operating  the  mercury  arc  in  a  quartz  tube,  vapor  pres- 
sures of  several  atmospheres  can  be  produced,  and  then  the  red 
lines  are  very  much  more  intense,  many  more  lines  have  be- 
come visible  in  the  mercury  spectrum,  and  the  light  is  far  less 
greenish  than  the  low-temperature  mercury  arc,  more  nearly 
white. 

Still  much  higher  temperatures  can  be  reached  in  the 
mercury  arc  in  an  ordinary  glass  tube  by  using  the  condenser 
discharge. 

I   have   here,   in   Fig.   44,  a  mercury-arc    tube   with   four 


LUMINESCENCE. 


121 


terminals  —  the  same  which  I  used  in  Fig.  34  for  showing 
simultaneously  the  mercury  arc  and  the  Geissler  discharge.  I 
connect  terminals  3  and  4  to  the  high  potential  terminals  of  a 
step-up  transformer,  but  shunt  a  small  condenser  C  across  3  and 
4;  you  see,  in  the  moment  where  I  connect  the  condenser,  the 
previously  existing  green  and  striated  Geissler  discharge  changes 


r=so  OHMS 


3 

r 

% 

\ 

\ 

-f- 

JL2JUL&L 

J>UP00Q 

0000 

roooo 

T 

III 

1-^-40 

1-7-40 

1 

r=.io  OHMS 

110  VOLTS 
60  CYCLES 

2  =  10  OHM 

110  VOLTS 
60  CYCLES 

*m 

FIG.  44. 

to  a  bright  pinkish-red  arc,  and  the  spectroscope  shows  that  the 
spectrum  lines  in  the  red  and  orange  have  greatly  increased  in 
number,  and  have  increased  in  intensity  beyond  that  of  the 
lines  in  the  green  and  blue,  and  the  color  of  the  light  therefore 
has  changed  from  green,  to  pinkish  red. 

We  have  here  in  the  same  mercury  tube  shown  diagram- 
matically  in  Fig.  44  all  three  forms  of  luminescence  of  mercury 
vapor:  the  high-current  low-voltage,  low-temperature  arc  of 


122  RADIATION,  LIGHT,  AND  ILLUMINATION. 

uniform  green  color,  from  1  to  2;  the  green  high-voltage  low- 
current  striated  Geissler  discharge,  from  2  to  3,  and  the  red  high- 
voltage  mercury  arc,  from  3  to  4. 

In  the  mercury  arc,  as  result  of  the  more  rapid  increase  of 
intensity  of  the  red  lines,  the  color  of  the  light  thus  changes 
with  increase  of  temperature  from  bluish  green  at  low  tempera- 
ture to  white  to  red  at  very  high  temperature,  that  is,  the  aver- 
age frequency  decreases  with  increase  of  temperature,  just  the 
reverse  from  what  is  the  case  with  temperature  radiation. 

The  change  in  the  distribution  of  the  power  of  radiation 
between  the  different  spectrum  lines,  with  change  of  tempera- 
ture, may  increase  the  efficiency  of  light  production  —  if  the 
lines  in  the  visible  range  increase  faster  than  in  the  ultra-red 
and  ultra-violet  —  or  may  decrease  —  if  the  visible  lines  in- 
crease slower  —  or  may  increase  in  some  temperature  range, 
decrease  in  some  other  temperature  range,  but  all  these  changes 
are  characteristic  of  the  luminescent  material,  and  do  not  obey 
a  general  law.  Thus  in  the  mercury  arc  the  efficiency  of  light 
production,  with  increase  of  temperature,  rises  to  a  maximum 
at  about  150  deg.  cent.,  then  decreases  to  a  minimum,  and  at  still 
higher  temperature  increases  to  a  second  maximum,  higher 
than  the  first  one,  possibly  between  600  and  800  deg.  cent.,  and 
then  decreases  again. 

52.  Essentially,  however,  the  efficiency  of  light  production 
by  the  arc  is  a  characteristic  of  the  material  of  the  arc  stream, 
and  thus  substances  which  give  a  large  part  of  their  radiation 
as  spectrum  lines  in  the  visible  range  —  as  calcium  —  give  a 
very  efficient  arc,  while  those  substances  which  radiate  most  of 
their  energy  as  lines  in  the  invisible,  ultra-violet  or  ultra-red  — - 
as  carbon  —  give  a  very  inefficient  arc.  The  problem  of  efficient 
light  production  by  the  arc  therefore  consists  in  selecting  such 
materials  which  give  most  of  their  radiation  in  the  visible  range. 

Carbon,  which  is  most  generally  used  for  arc  terminals,  is 
one  of  the  most  inefficient  materials :  the  carbon  arc  gives  very 
little  light,  and  that  of  a  disagreeable  violet  color;  it  is  practi- 
cally non-luminous,  and  the  light  given  by  the  carbon  arc  lamp 
is  essentially  incandescent  light,  temperature  radiation  of  the 
incandescent  tip  of  the  positive  carbon.  The  fairly  high  effi- 
ciency of  the  carbon  arc  lamp  is  due  to  the  very  high  tempera- 
ture of  the  black  body  radiator,  which  gives  the  light. 


LUMINESCENCE.  123 

The  materials  which  give  the  highest  efficiencies  of  light 
production  by  their  spectrum  in  the  arc  stream  arcs  mercury, 
calcium  and  titanium. 

As  mercury  vapor  is  very  poisonous,  the  mercury  arc  has  to 
be  enclosed  air-tight,  and  has  been  developed  as  a  vacuum  arc, 
enclosed  by  a  glass  or  quartz  tube.  Its  color  is  bluish  green. 

Calcium  gives  an  orange-yellow  light  of  very  high  efficiency, 
and  is  used  in  most  of  the  so-called  "flame-carbon  arcs,"  or 
"flame  arcs." 

Titanium  gives  a  white  light  of  extremely  high  efficiency. 
It  is  used  in  the  so-called  "luminous  arc,"  as  the  magnetite  arc 
in  direct-current  circuits,  the  titanium-carbide  arc  in  alternating- 
current  circuits. 

53.  Two  methods  exist  of  feeding  the  light-giving  material 
into  the  arc  stream : 

(1)  By  electro-conduction,  that  is,  using  the  material  as  the 
vapor  conductor  which  carries  the  current.     In  this  case,  it 
must  be  used  as  negative,  as  the  vapor  conductor  is  supplied 
from  the  negative;  such  arcs  are  called  "luminous  arcs." 

(2)  By  heat  evaporation;  in  this  case,  a  very  hot  arc  must  be 
used,  and  thus  usually  a  carbon  arc  is  employed.     As  the  posi- 
tive terminal  is  the  hottest,  the  material  is  mixed  with  the  car- 
bon of  the  positive  terminal,  and  as  negative  terminal  either  a 
plain  carbon,  or  also  an  impregnated  carbon  used;    such  arcs 
are  called  "flame  arcs." 

The  method  of  heat  evaporation  is  always  used  witri  calcium, 
since  no  stable  conducting  calcium  compound  is  known  which 
may  be  used  as  negative  arc  terminal.  With  titanium,  usually 
electro-conduction  is  employed,  that  is,  a  titanium  oxide-mag- 
netite mixture,  or  titanium  carbide,  used  as  negative  terminal, 
and  any  other  terminal,  as  copper  or  carbon,  as  positive  ter- 
minal. Titanium  can  also  be  introduced  by  heat  evaporation 
by  using  a  titanium-carbon  mixture  as  positive  terminal  or  as 
both  terminals  of  the  flame-carbon  arc. 

Both  methods  of  feeding  —  electro-conduction  and  heat  evapo- 
ration —  have  advantages  and  disadvantages. 

Electro-conduction  has  the  great  advantage  that  the  tem- 
perature of  the  terminals  is  immaterial,  as  heat  plays  no  part  in 
feeding  the  luminescent  material  into  the  arc  flame.  The  posi- 
tive terminal  of  the  arc  can  be  made  sufficiently  large  and  of 


124  RADIATION,  LIGHT,  AND  ILLUMINATION. 

such  material  as  not  to  consume  at  all,  and  the  trimming  of  the 
lamp  thus  reduced  to  the  replacing  of  one  electrode  only  —  the 
negative.  The  negative  electrode  also  can  be  made  so  large  as 
to  remain  fairly  cold,  and  therefore  consumes  only  at  the  very 
slow  rate  required  to  supply  the  arc  vapor,  but  does  not  con- 
sume by  combustion  or  heat  evaporation.  Thus  its  rate  of  con- 
sumption can  be  reduced  to  1  mm.  or  less  per  hour  (while  the 
open  carbon  arc  of  old  consumes  about  5  cm.  of  electrodes  per 
hour),  and  thereby  even  with  a  moderate  size  of  electrode  a  life 
of  electrodes  of  100  to  200  hr.  or  even  much  more  secured.  This 
method  of  feeding  thus  lends  itself  very  well  to  long-burning  arcs, 
as  they  are  almost  exclusively  used  for  American  street  lighting. 

By  electro-conduction  higher  efficiencies  can  be  reached  than 
by  heat  evaporation,  as  the  arc  vapor  stream  when  produced  by 
electro-conduction  can  be  made  to  consist  entirely  of  the  vapor 
of  the  luminescent  material,  as  when  using  metallic  titanium  as 
negative  terminal. 

A  disadvantage  of  the  method  of  feeding  the  arc  by  electro- 
conduction  is  the  much  greater  limitation  in  the  choice  of 
materials:  the  material  must  be  an  electric  conductor,  which  is 
stable  in  the  air,  and  reasonably  incombustible.  In  the  method 
of  feeding  by  heat  evaporation  any  material  can  be  used,  as 
it  is  mixed  with  carbon,  and  the  conductivity  is  given  by  the 
carbon.  Thus,  in  the  titanium  arc,  either  metallic  titanium  or 
titanium  carbide  or  sub  oxide  must  be  used,  but  the  most  com- 
mon titanium  compound,  Ti02,  or  rutile,  is  not  directly  suitable, 
since  it  is  a  non-conductor.  In  the  direct-current  titanium  arc, 
the  so-called  magnetite  arc,  a  solution  of  Ti02,  or  rutile,  in  mag- 
netite, Fe304,  which  is  conducting,  is  used,  that  is,  a  mixture  of 
rutile  with  a  considerable  weight  of  magnetite.  While  mag- 
netite also  gives  a  luminous  arc,  —  the  white  iron  spectrum,  — 
the  efficiency  of  the  iron  arc  is  lower  than  that  of  the  titanium 
arc,  and  the  efficiency  of  the  magnetite  arc  thus  lower  than  that 
of  the  pure  titanium  arc,  though  much  higher  than  that  of  the 
carbon  arc. 

Calcium  cannot  be  used  at  all  by  electro-conduction:  the 
only  more  common  conducting  calcium  compound  is  calcium 
carbide.  As  negative  terminal  calcium  carbide  gives  an  arc  of 
an  efficiency  far  superior  to  that  of  the  flame-carbon  arc,  but, 
as  calcium  carbide  disintegrates  in  the  air,  it  cannot  be  used. 


LUMINESCENCE.  125 

Still  greater  is  the  limitation  for  alternating  current;  in  this 
case  the  material,  in  addition  to  its  other  qualifications,  must 
have  such  a  high  boiling  point  as  to  maintain  a  steady  alternat- 
ing arc,  as  discussed  above.  Of  the  titanium  compounds  only 
titanium  carbide  seems  to  fulfill  this  requirement;  of  the  iron 
compounds,  apparently  none. 

54.  The  most  serious  disadvantage  of  the  use  of  electro- 
conduction  for  feeding  the  arc,  however,  has  been  the  inherently 
greater  unsteadiness  of  metal  arcs  compared  with  the  carbon 
arc.  It  is  this  feature  which  has  retarded  the  development 
of  true  luminous  arcs  until  recent  years,  that  is,  until  means 
were  found  to  produce  steadiness  by  eliminating  the  nickering 
of  the  negative  spot  by  the  admixture  of  a  more  refractory 
material,  — chromite  in  the  magnetite  arc, — and  eliminating 
the  unsteadiness  due  to  the  occasional  momentary  fading  out 
of  the  luminous  inner  core  of  the  arc  by  the  admixture  of  a  very 
small  amount  of  some  more  volatile  material. 

The  great  advantage  of  the  method  of  feeding  the  luminescent 
material  into  the  arc  flame  by  heat  evaporation,  mainly  from  the 
positive,  is  the  possibility  of  using  carbon  as  arc  conductor, 
which  gives  the  inherent  steadiness  of  the  carbon  arc,  and  thus 
has  led  to  the  development  of  this  type  of  high  efficiency  arc, 
the  flame  arc,  before  the  development  of  true  luminous  arcs. 

A  further  advantage  is  the  possibility  of  using  alternating 
current  equally  well  and  with  the  same  electrodes  as  used  with 
direct  current,  as  the  arc  is  a  carbon  arc  and  thus  operative  on 
alternating  current 

Another  advantage  is  the  great  choice  of  materials  available, 
since  practically  any  stable  compound,  whether  conducting  or 
not,  can  be  used  in  the  flame  carbon.  Thus  in  the  yellow-flame 
arc,  calcium  fluoride,  oxide  and  borates  are  used;  in  the  tita- 
nium arc,  the  oxide  (rutile)  or  the  carbide  may  be  used. 

The  most  serious  disadvantage  of  the  method  of  feeding  by 
heat  evaporation,  which  has  so  far  excluded  the  flame  arc  from 
general  use  for  American  street  illumination,  is  the  rapid  con- 
sumption of  the  electrodes  and  their  consequent  short  life. 
Since  the  luminescent  material  is  fed  into  the  arc  by  heat  evap- 
oration, the  electrodes  must  be  so  small  that  their  ends  are  raised 
to  arc  temperature,  and  thus  rapidly  consume  by  the  combus- 
tion of  the  carbon.  The  combustion  cannot  be  reduced  by 


126  RADIATION,  LIGHT,  AND  ILLUMINATION. 

excluding  the  air  by  enclosing  the  arc  with  an  almost  air-tight 
globe,  as  in  the  enclosed  carbon  arc,  since  the  luminescent 
material  leaves  the  arc  as  smoke,  and  by  depositing  on  the 
globe  rapidly  obstructs  the  light.  The  rate  of  consumption  of 
the  electrodes  thus  is  the  same  as  in  the  open  carbon  arc,  3  to 
5  cm.  (1  to  2  in.)  per  hour,  and  the  flame-carbon  arc  even  with 
very  great  length  of  carbon  thus  lasts  only  one  night,  that  is, 
requires  daily  trimming.  To  some  extent  this  difficulty  may 
be  reduced  by  using  the  same  air  again,  after  passing  it  through 
a  smoke-depositing  chamber  in  a  so-called  " circulating"  or 
"regenerative"  flame  lamp. 

The  mercury  arc,  being  enclosed  in  a  glass  tube,  necessarily 
must  always  be  fed  by  electro-conduction  from  the  negative. 
The  calcium  arc  is  always  fed  by  heat  evaporation  from  the 
carbon  positive,  with  a  carbon  negative,  or  from  positive  and 
negative,  by  using  flame  carbons  for  both  electrodes.  The 
titanium  arc  is  usually  fed  by  electro-conduction  from  the  neg- 
ative, but  also  by  heat  evaporation  from  the  positive  by  using 
a  titanium-flame  carbon. 

55.  As,  by  electro-luminescence,  electric  energy  is  converted 
more  directly  into  radiation,  without  heat  as  intermediary  form 
of  energy,  no  theoretical  limit  can  be  seen  to  the  possible  effi- 
ciency of  light  production  by  the  arc,  and  in  the  mercury,  cal- 
cium and  titanium  arcs,  efficiencies  have  been  reached  far  beyond 
those  possible  with  temperature  radiation.  Thus,  specific  con- 
sumptions of  0.25  watt  per  mean  spherical  candle  power  are 
quite  common  with  powerful  titanium  or  calcium  arcs,  and  even 
much  better  values  have  been  observed.  It  is  therefore  in  this 
direction  that  a  radical  advance  in  the  efficiency  of  light  pro- 
duction appears  most  probable.  At  present,  the  main  disad- 
vantage of  light  production  by  the  arc  is  the  necessity  of  an 
operating  mechanism,  an  arc  lamp,  which  requires  some  atten- 
tion, and  thereby  makes  the  arc  a  less  convenient  illuminant 
than,  for  instance,  the  incandescent  lamp,  and  especially  the 
limitation  in  the  unit  of  light:  the  efficiency  of  the  arc  decreases 
with  decrease  of  power  consumption,  and,  while  the  arc  is  very 
efficient  in  units  of  hundreds  or  thousands  of  candle  power,  its 
efficiency  is  much  lower  in  smaller  units,  and  very  small  units 
cannot  be  produced  at  all.  Thus,  for  instance,  while  a  500- 
watt  flame  arc  may  give  10  times  as  much  light  as  a  500-watt 


LUMINESCENCE.  127 

carbon  arc,  to  produce  by  a  flame  arc  the  same  amount  of  light 
as  given  by  a  500-watt  carbon  arc  requires  very  much  more  than 
one-tenth  the  power.  So  far  no  way  can  be  seen  of  maintaining 
the  efficiency  of  the  arc  down  to  such  small  units  of  light  as 
represented  by  the  16-  or  20-eandle  power  incandescent  lamp. 


LECTURE   VII. 
FLAMES    AS    ILLUMINANTS. 

56.  Two  main  classes  of  illuminants  exist:  those  producing 
radiation  by  the  conversion  of  the  chemical  energy  of  com- 
bustion—  the  flames — and  those  deriving  the  energy  of  radia- 
tion from  electric  energy  —  the  incandescent  lamp  and  the  arc 
lamp,  and  other  less  frequently  used  electric  illuminants. 

Flames. 

To  produce  light  from  the  chemical  energy  of  combustion, 
almost  exclusively  hydrocarbon  flames  are  used,  as  the  gas  flame, 
the  candle,  the  oil  lamp,  the  gasolene  and  kerosene  lamp,  etc.; 
that  is,  compounds  of  hydrogen  and  carbon  or  of  hydrogen, 
carbon  and  some  oxygen  are  burned.  The  hydrogen,  H,  com- 
bines with  the  oxygen,  0,  of  the  air  to  water  vapor,  H20,  and  the 
carbon,  C,  with  the  oxygen  of  the  air,  to  carbon  dioxide,  C02; 
or,  if  the  air  supply  is  insufficient,  to  carbon  monoxide,  CO,  a 
very  poisonous,  combustible,  odorless  gas  (coal  gas),  which 
thus  appears  in  all  incomplete  combustions  and  is  present,  also, 
as  intermediary  stage,  in  complete  combustion. 

The  mechanism  of  the  light  production  by  the  hydrocarbon 
flame  I  illustrate  here  on  the  luminous  gas  flame :  where  the  gas 
issues  from  the  burner  into  the  air,  it  burns  at  the  surface  of  the 
gas  jet.  By  the  heat  of  combustion  the  gas  is  raised  to  a  high 
temperature.  Most  hydrocarbons,  however,  cannot  stand  high 
temperatures,  but  split  up,  dissociate  into  simpler  hydro- 
carbons very  rich  in  hydrogen :  methane,  CH4,  and  in  free  carbon. 
The  carbon  particles  formed  by  this  dissociation  of  hydrocar- 
bon gas  float  in  the  burning  gases,  that  is,  in  the  flame,  and  are 
raised  to  a  high  temperature  by  the  heat  of  combustion  of  the 
gases,  thereby  made  incandescent,  and  radiate  light  by  tem- 
perature radiation;  until  ultimately,  at  the  outer  edge  of  the 
flame,  they  are  burned  by  the  oxygen  of  the  air,  and  thus 
destroyed.  We  can  see  these  carbon  particles,  which,  floating 

128 


FLAMES  AS  ILLUMINANTS.  129 

in  the  flame  in  anjncandescent  state,  give  the  light  if,  by  passing 
a  cold  porcelain  or  glass  plate  through  the  luminous  flame, 
we  suddenly  chill  it  and  thereby  preserve  the  carbon  particles 
from  combustion;  they  appear  then  on  the  plate  as  a  carbon 
deposit,  soot  or  lampblack.  The  light  given  by  the  luminous 
hydrocarbon  flame  thus  is  due  to  black-body  radiation,  and  the 
flame  makes  its  own  radiator,  and  afterwards  destroys  it  by 
combustion. 

To  give  a  luminous  flame,  the  hydrocarbon  must  be  suffi- 
ciently rich  in  carbon  to  split  off  carbon  at  high  temperatures. 
Thus  methane,  CH4,  does  not  give  a  luminous  flame,  since  it  con- 
tains the  smallest  amount  of  carbon  which  can  combine  with 
hydrogen,  and  therefore  does  not  deposit  carbon  at  high  tem- 
peratures. Ethylene,  however,  C2H4,  which  is  the  foremost 
light  giving  constituent  of  illuminating  gas,  dissociates  in  the 
flame  into  CH4  and  C,  and  thus  gives  a  luminous  flame,  as  half 
of  its  carbon  is  set  free  and  gives  the  incandescent  radiator. 

If,  however,  the  hydrocarbon  is  very  rich  in  carbon,  the 
amount  of  deposited  carbon  becomes  so  large  that  the  energy 
of  combustion  of  the  remaining  hydrocarbon  is  not  sufficient  to 
raise  the  carbon  to  very  high  temperatures,  the  luminosity 
therefore  again  decreases,  the  flame  becomes  reddish  yellow, 
and  a  large  amount  of  carbon  escapes  from  the  flame  uncon- 
sumed,  as  smoke  or  soot,  that  is,  the  flame  becomes  smoky. 

To  show  you  this,  I  pour  some  gasolene  and  some  benzol  in 
small  glass  dishes.  The  gasolene,  having  2J  hydrogen  atoms 
per  carbon  atom,  burns  with  a  luminous  flame  and  very  little 
smoke.  The  benzol,  having  only  one  hydrogen  atom  per  carbon 
atom,  burns  with  a  reddish-yellow  flame,  pouring  out  masses 
of  black  smoke. 

The  proportion  between  the  hydrogen  and  carbon  required 
to  give  a  luminous  non-smoky  flame,  therefore  can  be  varied 
only  within  narrow  limits:  too  little  carbon  gives  a  less  lumi- 
nous or  non-luminous  flame,  too  much  carbon  a  smoky  reddish 
flame. 

Hydrocarbons  exist  having  almost  any  proportion  between 
hydrogen  and  carbon,  from  a  maximum  of  four  hydrogen  atoms 
to  one  carbon  in  methane,  CH4,  to  practically  pure  carbon  in 
anthracite  coal.  Some  of  them  are  shown  in  the  following 
table,  with  the  number  of  hydrogen  atoms  per  carbon  atom 


130 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


added  in  column  a,  and  the  percentage  of  carbon  which  is  de- 
posited by  dissociation,  in  column  b  ;*  a  thus  may  be  called  the 
luminosity  index  of  the  hydrocarbon. 


HYDROCARBONS. 


Name. 

State. 

Formula. 

Lumi- 
nosity 
Index 

(a). 

Car- 
bon 

Index 
(ft). 

Paraffines: 
Methane 

Gas. 
do.. 

CH4 
C2H6 

C3H8 
r4H10 

^5n!2 

C«H14 
C10H22 

^14^30 

C20H42 

U24±150 

C2H4 
C2H2 

C.H6 
C10H8 

C14H10 

approx. 

4.0 
3.0 

2.67 
2.5 
2.4 

2.33 
2.2 
2.14 

2.1 
2.08 

2 
1 

1 

0.8 
0.71 

0 
0.25 

0.333 
0.375 
0.40 

0.417 
0.45 
0.464 

0.475 
0.479 

0.50 
0.75 

0.75 
0.80 
0.821 

Ethane 

Propane 

.   do... 

Butane 

.  .   do... 

Pentane     .               ... 

Liquid. 

..do.. 
.  .  .do.... 

Gasolene  

Kerosene   

Mineral  oil  
Vaseline  

..  .do.... 

Solid, 
do 

Paraffine 

Olefines: 
Ethylene  

Gas. 
Gas. 

Liquid. 
Solid, 
do.. 

Acetylenes: 
Acetylene 

Benzols: 
Benzol 

Naphthalene 

Anthracene 

57.  The  proportion  between  carbon  and  hydrogen  required  to 
give  a  luminous  non-smoky  flame  somewhat  depends  on  the 
size  of  the  flame,  and,  with  a  larger  size,  a  higher  proportion  of 
hydrogen  is  required  to  avoid  smoke  than  with  a  smaller  flame, 
as  in  the  latter,  due  to  the  larger  surface  compared  with  the 
volume,  the  combustion  is  more  rapid.  I  show  you  this  on  the, 
gas  flame :  admitting  a  little  gas,  I  get  a  small  flame,  which  does 
not  smoke,  but  if  I  open  the  stop-cock  wide  I  get  a  large  and 
smoky  flame. 

With  a  moderate-sized  flame  without  artificial  ventilation, 
from  30  to  40  per  cent  of  the  carbon  must  be  deposited  to  give 
good  luminosity  without  smoke.  This  corresponds  to  a  value  a 

*  Every  four  hydrogen  atoms  retain  one  carbon  atom,  while  the  rest  of  the 
carbon  is  set  free. 


FLAMES  AS  ILLUMINANTS.  131 

between  2.4  and  somewhat  less  than  three  hydrogen  atoms  per 
carbon  atom.  Ethane,  C2H6,  with  a  =  3,  still  gives  a  luminous 
flame,  but  of  somewhat  lower  luminosity,  and,  on  the  other 
side,  the  gasolene  flame,  a  =  2.33,  is  slightly  smoky.  However, 
in  very  small  flames  in  which  the  surface  is  larger  compared 
with  the  volume,  and  the  combustion  thus  very  rapid,  higher 
percentages  of  carbon  can  be  used  without  smoke.  Thus  the 
flame  of  the  parafnne  candle  a  =  2.08  is  still  smokeless  but 
begins  to  smoke  if  it  gets  large,  and  in  extremely  small  flames, 
J  in.  or  less  diameter,  even  acetylene,  a  =  1,  gives  smokeless 
combustion. 

Increase  of  the  rapidity  of  combustion  by  increasing  the  sur- 
face of  the  flame  by  using  a  flat  or  hollow  cylindrical  burner, 
and  increasing  the  air  supply  by  artificial  draft,  as  by  a  chimney, 
gives  smokeless  flames  even  up  to  b  =  50,  or  one  carbon  atom 
to  two  hydrocarbon  atoms,  a  =  2. 

Thus  kerosene,  which,  due  to  its  high  carbon  content  a  =  2.14, 
smokes  badly,  except  in  very  small  flames,  is  burned  smoke- 
lessly  in  lamps  with  chimneys  and  flat  or  hollow  round  burners, 
and  then  gives  a  high  light  intensity :  with  the  rapid  air  supply 
and  the  large  surface  of  the  thin  flame,  the  combustion  is  very 
rapid,  a  part  of  the  free  carbon  is  immediately  consumed,  the 
temperature  is  high,  and  thus  the  free  carbon  heated  sufficiently 
to  give  considerable  light,  and  to  consume  completely  when 
leaving  the  flame.  With  a  hydrocarbon  still  richer  in  carbon, 
as  acetylene  or  benzol  a  =  1,  artificial  draft  and  large  flame 
surface  are  no  longer  sufficient  to  give  smokelessness,  and  the 
total  range  of  hydrocarbons  which  can  be  burned  with  lumi- 
nous flames  and  without  smoke  thus  is  between  from  three  to 
two  hydrogen  atoms  per  carbon  atom. 

Hydrocarbons  which  are  too  rich  in  carbon  to  be  burned 
smokelessly,  as  acetylene  or  benzol,  obviously  can  be  burned 
with  a  smokeless  luminous  flame  by  mixing  them  in  the  proper 
proportions  with  hydrocarbons  deficient  in  carbon,  which  latter 
by  themselves  would  give  a  non-luminous  or  nearly  non-lumi- 
nous flame.  Thus  a  mixture  of  one  volume  of  acetylene,  C2H2, 
with  three  volumes  of  methane,  3  CH4,  (the  number  of  mole- 
cules of  gases  are  proportional  to  their  volumes),  gives  a  non- 
smoky  luminous  flame:  5  C  to  14  H,  or  a  =  2.8. 

Such  hydrocarbons  as  acetylene,  benzol,  etc.,  which  are  rich 


132  RADIATION,  LIGHT,  AND  ILLUMINATION. 

in  carbon,  are  used  for  enriching  poor  gas,  that  is,  making  it 
more  luminous :  gas  which  gives  little  free  carbon,  as  water-gas 
(which  is  rich  in  H  and  CO  — both  giving  non-luminous  flames), 
and  which  therefore  would  give  a  non-luminous  or  only  slightly 
luminous  flame,  thus  is  improved  in  its  light-giving  quality 
by  admixture  of  acetylene,  etc. 

58.  If  the  hydrocarbon  contains  oxygen,  as  alcohol,  C2H60, 
etc.,  the  presence  of  oxygen  atoms  reduces  the  luminosity  or 
the  tendency  to  smoke,  by  taking  care  of  a  corresponding  num- 
ber of  carbon  atoms:  the  most  stable  compound  is  CO,  and 
water  vapor,  H20,  as  well  as  carbon  dioxide,  C02,  are  reduced 
by  carbon  at  high  temperature  with  the  formation  of  carbon 
monoxide,  CO.  During  the  dissociation  of  the  hydrocarbon  in 
the  flame,  each  oxygen  atom  takes  up  one  carbon  atom,  form- 
ing CO,  which  burns  with  a  non-luminous  flame.  In  approxi- 
mately estimating  the  luminosity  or  the  tendency  to  smoke  of  a 
hydrocarbon  containing  oxygen,  for  each  oxygen  atom  one  car- 
bon atom  is  to  be  subtracted.  To  illustrate  this  I  pour  some 
aldehyde,  C2H40,  and  some  amyl  acetate,  C7H1402,  in  small  glass 
dishes  and  ignite  them.  In  both  the  ratio  of  hydrogen  to  car- 
bon atom  is  a  =  2,  corresponding  to  a  luminous  but  smoky 
flame.  You  see,  however,  that  the  aldehyde  burns  with  a  per- 
fectly non-luminous  flame :  we  have  to  put  out  the  light  to  see 
it;  while  the  amyl  acetate  burns  with  a  luminous,  non-smoky 
flame.  Applying  above  reasoning,  the  oxygen  accounts  for  one 
carbon  atom  in  the  aldehyde :  C2H40  =  CO  +  CH4,  and  in  CH4 : 
a  =  4,  corresponding  to  a  non-luminous  flame,  as  observed.  In 
amyl  acetate,  the  two  oxygen  atoms  take  up  two  carbon  atoms : 
C7H1402  =  2  CO  +  C5H14,  and  the  ratio  of  hydrogen  to  carbon 
atoms  is  a  =  2.8,  or  b  =  30,  corresponding  to  a  luminous  non- 
smoky  flame,  as  observed. 

The  same  effect  as  given  by  oxygen  contained  in  the  hydro- 
carbon molecule  obviously  is  obtained  by  mixing  oxygen  or 
air  with  the  hydrocarbon.  I  illustrate  this  on  the  bunsen 
flame :  closing  the  air  supply,  I  have  an  ordinary  luminous  and 
somewhat  smoky  gas  flame.  I  now  gradually  admit  air,  and  you 
see  first  the  smoke  disappear,  and  then  the  luminosity  decreases, 
and  first  the  lower  part,  and  then  the  entire  flame,  becomes 
non-luminous.  When  the  luminosity  has  just  disappeared,  the 
amount  of  air  mixed  with  the  gas  is  just  sufficient  to  take  up 


FLAMES  AS  ILLUMINANTS.  133 

all  the  carbon  as  CO,  which  would  deposit  otherwise  and  give 
the  incandescent  radiator,  but  it  is  far  below  the  amount  required 
for  complete  combustion,  and,  by  still  further  increasing  the  air 
supply,  you  see  the  rapidity  of  combustion  still  further  increase, 
as  shown  by  the  decreasing  size  of  the  flame.  With  increasing 
air  supply,  the  size  of  the  flame  very  greatly  decreases,  and,  as 
the  same  total  heat  is  produced  by  the  combustion,  this  means 
that  the  heat  is  concentrated. in  a  smaller  volume,  that  is,  the 
temperature  of  the  flame  is  increased,  in  other  words,  the  non- 
luminous  bunsen  flame  is  of  higher  temperature  than  the  lumi- 
nous gas  flame. 

Hydrocarbons  which  are  too  rich  in  carbon  to  burn  without 
smoke,  as  acetylene,  can  be  burned  with  a  smokeless  flame  by 
mixing  them  with  oxygen  or  with  air.  Acetylene  is  always 
burned  in  this  manner,  and  all  acetylene-gas  burners  are  con- 
structed so  as  to  take  in  air  with  the  acetylene  gas  before  com- 
bustion, that  is,  are  small  bunsen  burners  or  similar  thereto. 
Since  the  temperature  of  the  bunsen  flame,  due  to  the  more 
rapid  combustion  resulting  from  the  mixture  with  air,  is  higher 
than  that  of  the  ordinary  gas  flame,  and  in  the  acetylene  flame 
in  the  acetylene  air  mixture  a  large  part  of  the  carbon  is  also 
immediately  burned,  the  temperature  of  the  acetylene  flame  is 
very  high,  and  the  deposited  carbon  therefore  raised  to  a  very 
high  temperature,  much  higher  than  in  the  ordinary  gas  flame, 
and,  as  the  result  of  the  higher  temperature,  the  black-body 
radiation  of  the  free  carbon  in  the  acetylene  flame  is  far  more 
efficient,  and  of  much  whiter  color  than  in  the  ordinary  gas  flame. 

Thus  the  hydrocarbons  which  are  very  rich  in  carbon,  as 
acetylene,  benzol,  naphthalene,  etc.,  if  burned  smokelessly  by 
mixture  with  air,  give  whiter  and  more  efficient  flames,  due 
to  their  higher  temperature.  Especially  is  this  the  case  with 
acetylene,  as  the  energy  of  combustion  of  acetylene  is  higher 
than  that  of  other  hydrocarbons  of  the  same  relative  propor- 
tions of  hydrogen  and  carbon:  acetylene  being  endothermic, 
that  is,  requiring  energy  for  its  formation  from  the  elements. 

59.  Since,  as  discussed  in  Lecture  VI,  chemical  luminescence 
usually  occurs  where  intense  chemical  reactions  take  place  at  high 
temperatures,  —  and  this  is  the  case  in  the  flame,  —  chemical 
luminescence  of  the  flame  gases  must  be  expected  in  the  hydro- 
carbon flame.  It  does  occur,  but  does  not  contribute  anything 


134  RADIATION,  LIGHT,  AND  ILLUMINATION. 

to  the  light  production,  since  the  spectra  of  hydrogen  and  of 
carbon  (or  CO  and  CH4)  are  practically  non-luminous.  The 
luminescence  of  the  hydrocarbon  flame  therefore  can  be  observed 
only  with  those  hydrocarbons  which  are  sufficiently  poor  in  car- 
bon as  not  to  deposit  free  carbon,  as  methane,  alcohol,  etc.,  or 
in  which,  by  the  admixture  of  air,  the  deposition  of  free  carbon 
and  thereby  the  formation  of  an  incandescent  radiator,  is 
avoided,  as  in  the  bunsen  flame.  In  this  case,  the  blue  color  of 
the  chemical  luminescence  of  carbon-flame  gases  is  seen:  all 
non-luminous  hydrocarbon  flames  are  blue. 

60.  While  light,  and  radiation  in  general,  can  also  be  pro- 
duced by  the  combustion  of  other  materials  besides  hydro- 
carbons, industrially  other  materials  are  very  little  used. 

Burning  magnesium  gives  a  luminous  flame  of  extremely 
high  brilliancy  and  whiteness.  Its  light  is  largely  due  to  tem- 
perature radiation,  and  the  flame  makes  its  own  incandescent 
radiator;  but  unlike  the  hydrocarbon  flame,  in  which  the  radiator 
is  again  destroyed  by  combustion,  the  incandescent  radiator  of 
the  magnesium  flame  is  the  product  of  combustion,  magnesia, 
MgO,  and  escapes  from  the  flame  as  white  smoke.  While,  how- 
ever, in  the  hydrocarbon  flame  the  incandescent  radiator  is  a 
black  body, — carbon, —  giving  the  normal  temperature  radiation, 
the  radiator  of  the  magnesium  flame,  magnesia,  is  a  colored 
radiator,  and  its  radiation  is  deficient  in  intensity  in  the  ultra- 
red,  and  very  high  in  the  visible  range,  and  thereby  of  a  much 
higher  efficiency  than  given  by  black-body  radiation.  The 
magnesium  flame  therefore  is  far  more  efficient  than  the  hydro- 
carbon flame,  and  its  light  whiter. 

So  also  burning  aluminum,  zinc,  phosphorus,  etc.,  give  lu- 
minous flames  containing  incandescent  radiators  produced  by 
the  combustion:  alumina,  zinc  oxide,  etc. 

Superimposed  upon  the  temperature  radiation  of  the  incan- 
descent radiator  of  those  flames  is  the  radiation  of  chemical 
luminescence.  Since,  however,  magnesium,  zinc,  aluminum, 
give  fairly  luminous  spectra,  in  these  flames  the  chemical  lumi- 
nescence contributes  a  considerable  part  of  the  light,  and  where 
the  luminescent  light,  that  is,  the  metal  spectrum,  is  of  a  marked 
color  —  as  green  with  zinc  —  the  flame  of  the  burning  metal 
also  is  colored.  Hence  burning  zinc  gives  a  greenish-yellow 
flame,  burning  calcium  an  orange -yellow  flame,  etc. 


FLAMES  AS  ILLUMINANTS.  135 

Obviously,  where  during  the  combustion  no  solid  body  is 
formed,  the  light  given  by  the  flame  is  entirely  chemical  lumi- 
nescence. Thus  burning  sulphur  gives  a  blue  flame,  and,  if 
the  temperature  of  combustion  is  increased  by  burning  the 
sulphur  in  oxygen,  it  gives  a  fairly  intense  light,  of  violet  color, 
and  a  radiation  which  is  very  intense  in  the  ultra-violet.  Thus 
before  development  of  the  ultra-violet  electric  arcs,  as  the  iron 
arc,  for  the  production  of  ultra-violet  radiation  lamps  were  used, 
burning  carbon  bisulphide,  CS2,  in  oxygen.  Carbon  bisulphide, 
has  the  advantage  over  sulphur  that,  as  liquid,  it  can  easier  be 
handled  in  a  lamp,  and  especially  the  combustion  of  carbon 
(without  adding  much  to  the  light,  due  to  the  non-luminous 
character  of  the  carbon  spectrum)  greatly  increases  the  flame 
temperature,  and  thereby  the  intensity  of  the  radiation. 

Flames  with  Separate  Radiator. 

61.  The  hydrocarbons  are  the  only  sources  of  chemical 
energy  which  by  their  cheapness  are  available  for  general  use 
in  light  production.  Carbon,  however,  is  a  black-body  radiator, 
and  its  efficiency  of  light  production  therefore  very  low,  es- 
pecially at  the  relatively  low  temperature  of  the  luminous 
hydrocarbon  flame,  and  such  flames  are,  therefore,  low  in 
efficiency  of  light  production,  with  the  exception  of  the  acety- 
lene flame  and  other  similar  flames. 

Separating  the  conversion  into  light  from  the  heat  production; 
that  is,  using  the  hydrocarbon  flame  merely  for  producing  heat, 
and  using  a  separate  radiator  for  converting  the  heat  into  light, 
offers  the  great  advantage 

(1)  That  a  colored  body  can  be  used  as  radiator,  and  thereby 
a  higher  efficiency  of  light  production,  at  the  same  temperature, 
secured,  by  selecting  a  body  deficient  in  invisible  and  thereby 
useless  radiation. 

(2)  That  the  rapidity  of  combustion  can  be  greatly  increased 
by  mixing  the  hydrocarbon  with  air  in  a  bunsen  burner,  and 
thereby  the  temperature  of  the  flame  increased,  which  results 
in  a  further  increase  of  the  efficiency  of  light  production. 

Thus,  by  the  use  of  suitable  external  radiators,  in  a  non- 
luminous  hydrocarbon  flame,  far  higher  efficiencies  of  light 
production  are  reached  than  by  the  use  of  the  luminous  hydro- 
carbon flame. 


136  RADIATION,  LIGHT,  AND  ILLUMINATION. 

The  first  use  of  external  radiators  probably  was  the  use  of  a 
lime  cylinder  in  a  hydro-oxygen  flame,  in  the  so-called  "lime 
light/'  for  producing  very  large  units  of  light. in  the  days  before 
the  electric  arc  was  generally  available. 

In  the  last  quarter  of  a  century  the  external  radiator  has 
come  into  extended  use  in  the  Welsbach  mantle;  the  hydro- 
carbon is  burned  in  a  bunsen  burner,  that  is,  mixed  with  air,  so 
as  to  get  a  non-luminous  flame  of  the  highest  temperature,  and 
in  this  flame  is  immersed  a  cone-shaped  web  of  a  highly  effi- 
cient colored  radiator:  thoria  with  a  small  percentage  of  ceria, 
etc.,  the  so-called  "mantle."  The  higher  temperature,  com- 
bined with  the  deficiency  of  radiation  in  the  invisible  range,  ex- 
hibited by  this  colored  radiator,  results  in  an  efficiency  of  light 
production  several  times  as  high  as  that  of  the  luminous  gas 
flame.  The  distribution  of  intensity  in  the  spectrum  of  the 
Welsbach  mantle  obviously  is  not  that  of  black-body  radiation, 
but  differs  therefrom  slightly,  and  the  radiation  is  somewhat 
more  intense  in  the  greenish  yellow,  that  is,  the  light  has  a 
slightly  greenish-yellow  hue. 

The  Welsbach  mantle  is  very  interesting  as  representing  the 
only,  very  extensive  industrial  application  of  colored  radiation. 


LECTURE  VIII. 

ARC    LAMPS    AND    ARC    LIGHTING. 

Volt- Ampere  Characteristics  of  the  Arc. 

62.  The  voltage  consumed  by  an  arc,  at  constant  current, 
increases  with  increase  of  arc  length,  and  very  closely  propor- 
tional thereto.  Plotting  the  arc  voltage,  e,  as  function  of  the 


190 
180 
170 
160 
150 
140 
130 
120 
110 
100 
00 
80 
70 
60 
50 
'40 
30 
20 
10 


I.fi6 
0[5 


25 
1  0 


FIG.  45. 

arc  length,  I,  we  get  tor  every  value  of  current,  i,  a  practically 
straight  line,  as  shown  for  the  magnetite  arc  in  Fig.  45,  for  values 
of  current  of  1,  2,  4  and  8  amperes.  These  lines  are  steeper 

137 


138 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


for  smaller  currents,  that  is,  low-current  arcs  consume  a  higher 
voltage  for  the  same  length  than  high-current  arcs,  the  in- 
crease being  greater  the  longer  the  arc.  These  lines  in  Fig.  45 
intersect  in  a  point  which  lies  at  I  =  —  0.125  cm.  =  —  0.05  in. 
and  e  =  30  volts;  that  is,  the  voltage  consumed  by  the  arc 
consists  of  a  part,  e0  =  30  (for  the  magnetite  arc),  which  is  con- 


F;G.  46. 

stant,  that  is,  independent  of  the  arc  length  and  of  the  cur- 
rent in  the  arc,  but  different  for  different  materials,  and  a 
part,  ev  which  is  proportional  to  the  arc  length,  Z,  or  rather  to 
the  arc  length  plus  a  small  quantity,  1L=  0.125  (for  the  magne- 
tite arc):  e^  =  \(l  +  0.125),  and  depends  upon  the  current, 
being  the  larger  the  smaller  the  current. 

Plotting  the  arc  voltage,  e,  as  function  of  the  current,  i,  we 
get  curves  which  increase  with  decrease  of  current,  the  increase 
being  greater  the  longer  the  arc,  as  shown  in  Fig.  46,  for  the 


ARC  LAMPS  AND  ARC  LIGHTING.  139 

magnetite  arc,  for  I  =  0.3,  1.25,  2.5,  3.75  cm.  =  0.125,  0.5, 1  and 
1.5  in.  Subtracting  from  the  voltage,  6,  in  Fig.  46,  the  con- 
stant part,  e0  =  30  volts,  which  apparently  represents  the 
terminal  drop  of  voltage,  that  is,  the  voltage  which  supplies 
the  energy  used  in  producing  the  conducting  vapor  stream 
at  the  negative,  and  the  heat  at  the  positive  terminal,  leaves 
the  voltage,  el  =  e  —  eQJ  as  the  voltage  consumed  in  the  arc 
stream. 

The  curves  of  arc-stream  voltage,  ev  as  function  of  the  cur- 
rent, ij  in  Fig.  46,  can  with  approximation  be  expressed  by 

k 
cubic  hyperbolas:  e^i  =  kz2;  or,  el  =— £j  and  since  we  find  for 

Vi 

constant  value  of  current:  el  =  k^  (I  +  0.12),  as  function  of 
arc  length  and  current,  i,  the  voltage  of  the  arc  stream  is  ex- 
pressed by :  k  (I  +  I) 

ei  = TT1-'  (1 


and  the  total  arc  voltage  by : 

,  *(*+*,: 


(2) 


where  e0,  k  and  Zt  are  constants  of  the  terminal  material  (k,  how- 
ever, varies  with  the  gas  pressure  in  the  space  in  which  the  arc 
exists). 

This  equation  (2)  represents  the  arc  characteristics  with 
good  approximation,  except  for  long  low-current  arcs,  which 
usually  require  a  higher  voltage  than  calculated,  as  might  be 
expected  from  the  unsteady  nature  of  such  long  thin  arcs. 

The  equation  (2)  can  be  derived  from  theoretical  reasoning 
as  follows:  Assuming  the  amount  of  arc  vapor,  that  is,  the 
volume  of  the  conducting  vapor  stream,  as  proportional  to  the 
current,  and  the  heat  produced  at  the  positive  terminal  also  as 
proportional  to  the  current,  the  power  p0  required  to  produce 
the  vapor  stream  and  the  heating  of  the  positive  terminal  is 
proportional  to  the  current,  i\  and,  as  the  power  is  p0  =  eQi,  it 
follows  that  the  voltage,  e0,  consumed  at  the  arc  terminals  is 
constant. 

The  power  consumed  in  the  arc  stream  :  pl  =  ej,,  is  given  off, 
by  heat  conduction,  convection,  and  by  radiation,  from  the  sur- 


140  RADIATION,  LIGHT,  AND  ILLUMINATION. 

face  of  the  arc  stream,  and  thus,  as  the  temperature  of  the  arc 
stream  is  constant,  and  is  that  of  the  boiling  point  of  the  arc 
vapor,  the  power  pl  consumed  in  the  arc  stream  is  proportional 
to  its  surface,  that  is,  to  the  product  of  arc  diameter  ld  and  arc 
length  I,  or  rather  the  arc  length  I  increases  by  a  small  quantity 
lv  which  allows  for  the  heat  carried  away  to  the  electrodes.  As 
the  diameter  ld  is  proportional  to  the  square  root  of  the  section 
of  the  arc  stream,  and  the  section  of  the  arc  stream,  or  the 
volume  of  the  arc  vapor,  was  assumed  as  proportional  to  the 
current,  i,  the  arc  diameter  is  proportional  to  the  square  root 
of  the  current,  and  the  power  pt  consumed  in  the  arc  stream  thus 
is  proportional  to  the  square  root  of  the  current,  i,  and  to  (I  +  IJ  ; 

thatis'  p^kVid  +  lJ; 

and  since  pl  =  ej, 


which  is  equation  (1),  and  herefrom,   since  e  =  e0  +  eir  follows 
equation  (2). 

63.  Since  e0  represents  the  power  consumed  in  producing  the 
vapor  stream  and  the  heating  of  the  positive  terminal,  and  k 
the  power  dissipated  from  the  arc  stream,  e0  and  k  are  different 
for  different  materials,  and  in  general  higher  for  materials  of 
higher  boiling  point  and  thus  higher  arc  temperatures.  It  is, 
approximately, 

e0  =  13  volts  for  mercury, 

=  16  volts  for  zinc  and  cadmium, 
=  30  volts  for  magnetite, 
=  36  volts  for  carbon, 

k  =  31  for  magnetite  (123  in  inch  measure), 
=  35  for  carbon  (130  in  inch  measure). 

The  magnetite  arc,  of  which  the  characteristics  are  shown  in 
Figs.  45  and  46,  thus  can  be  represented  by: 

'  (3) 


The  least  agreement  with  the  theoretical  curve  (2)  is  shown  by 
the  carbon  arc.  This  may  be  expected  from  the  exceptional 
character  of  the  carbon  arc,  as  discussed  in  Lecture  VI.  Plot- 


ARC  LAMPS  AND  ARC  LIGHTING. 


141 


ting,  in  Fig.  47,  the  voltage,  e,  consumed  by  a  carbon  arc,  at 
constant  values  of  current  i,  as  function  of  the  arc  length  Z,  — 
as  done  for  the  magnetite  arc  in  Fig.  45,  —  when  using  only  the 
observation  for  arc  length  of  0.25  in.  and  over,  we  get  fairly 
satisfactory  straight  lines,  which  intersect  at  the  point,  giving 
e0  =  36  volts,  but  I,  =  -  0.8  cm.  =  -  0.33  in.;  that  is,  a 
value  much  greater  than  for  any  other  arc.  For  short  arc 


VOLTS 

150- 


•100 


2 


LE 


-20- 


25 


3  "5  cn 
1J5  IN. 


FIG.  47. 

lengths,  however,  the  observed  values  of  voltage  drop  below 
the  straight  line,  as  shown  in  Fig.  47,  and  converge  towards  a 
point,  at  zero  arc  length,  or  e0'  =  28  volts.  This  looks  as  if,  of 
the  potential  drop  of  e0  =  36  volts  of  the  carbon  arc,  only  a 
part,  e0'  =  28  volts,  occurs  at  the  surface  of  the  terminals,  and 
the  remaining  part,  e"  =  8  volts,  occurs  in  the  space  within 
a  short  distance  from  the  terminal  surface.  If  then  the  arc 
length  is  decreased  to  less  than  the  distance  within  which  the 
terminal  drop  e"  occurs,  the  arc  meets  only  a  part  of  this  ter- 
minal drop  e",  and,  for  very  short  arc  length,  only  the  terminal 
drop  e0'  occurs.  Possibly  the  voltage  e0'  =  28  is  consumed  at 
the  negative  terminal  in  producing  the  conducting  vapor  stream, 


142          RADIATION,  LIGHT,  AND  ILLUMINATION. 

while  the  voltage  e"  =  8  is  consumed  by  the  moving  vapor 
stream  in  penetrating  a  layer  of  dead  carbon  vapor  formed  by 
heat  evaporation  from  the  positive  terminal,  and  surrounding 
this  terminal. 

Stability  Curves  of  the  Arc. 

64.  From  the  volt-ampere  characteristic  of  the  arc,  as  rep- 
resented by  equation  (2)  and  reproduced  in  Fig.  48  as  Curve  I, 
for  a  magnetite  arc  of  1.8  cm.  (about  0.75  in.)  length,  it  follows 
that  the  arc  is  unstable  on  constant  potential  supply,  as  the, 
voltage  consumed  by  the  arc  decreases  with  increase  of  current 
and,  inversely,  a  momentary  increase  of  current  decreases  the 
consumed  voltage,  and,  on  constant  voltage  supply,  thereby 
increases  the  current,  still  further  decreases  the  arc  voltage 
and  increases  the  current,  and  the  arc  thus  short  circuits;  or  a 
momentary  decrease  of  current  increases  the  required  voltage 
and,  at  constant  supply  voltage,  continues  to  decrease  the  cur- 
rent and  thus  increase  still  further  the  required  voltage,  that  is, 
the  arc  goes  out. 

On  constant  voltage  supply  only  such  apparatus  can  operate 
under  stable  conditions  in  which  an  increase  of  current  requires 
an  increase,  and  a  decrease  of  current  a  decrease  of  voltage, 
and  thus  checks  itself. 

Inserting  in  series  with  the  arc,  curve  I,  in  Fig.  48,  a  constant 
resistance  of  10  ohms,  the  voltage  consumed  by  this  resistance, 
e  =  ir,  is  proportional  to  the  current,  and  given  by  the  straight 
line  II.  Adding  this  voltage  to  the  arc  voltage  curve  I,  gives 
the  total  voltage  consumed  by  the  arc  and  its  series  resistance, 
as  curve  III.  In  curve  III,  the  voltage  decreases  with  increase 
of  current,  for  values  of  current  below  i0  =  2.9  amperes,  and  the 
arc  thus  is  unstable  for  these  low  currents,  while  for  values  of 
current  larger  than  i0  =  2.9  amperes,  the  voltage  increases  with 
increase  of  current.  The  point  i0  =  2.9  amperes  thus  separates 
the  unstable  lower  part  of  the  curve  III  from  the  stable  upper 
part.  With  a  series  resistance  of  r  =  10  ohms,  a  1.8-cm.  mag- 
netite arc  thus  requires  at  least  e  =  117  volts  supply  voltage, 
and  i0  =  2.9  amperes  for  steady  operation.  With  a  larger 
series  resistance,  as  r  =  20  ohms,  represented  by  curve  II'  and 
III',  a  larger  supply  voltage  is  required,  but  smaller  currents  can 
be  operated ;  with  a  lower  series  resistance,  r  =  5  ohms,  curves 


ARC  LAMPS  AND  ARC  LIGHTING. 


143 


II"  and  III",  larger  currents  are  required  for  stable  operation, 
but  a  lower  supply  voltage  is  sufficient. 

When  attempting  to  operate  an  arc  close  to  the  stability  limit, 
i0,  where  a  small  variation  of  voltage  causes  a  large  variation  of 
current,  the  operation  of  the  arc  is  unsatisfactory,  that  is,  the 


FIG. 


current  drifts;  small  variations  of  the  resistance  of  the  arc 
stream,  and  thereby  of  the  voltage  consumed  by  the  arc,  cause 
excessive  fluctuations  of  the  current.  These  pulsations  of  cur- 
rent can  be  essentially  reduced  by  using  a  large  inductance 
in  series  with  the  arc,  and  an  arc  can  be  operated  very  much 
closer  to  its  stability  limit  if  its  series  resistance  is  constructed 
highly  inductive,  that  is,  wound  on  an  iron  core.  Obviously, 


144  RADIATION,  LIGHT,  AND  ILLUMINATION. 

no  series  inductance  can  extend  stable  operation  beyond  the 
stability  point  %. 

At  the  stability  limit  iQJ  the  resultant  characteristic  III  in 
Fig.  48  is  horizontal,  that  is,  the  slope  of  the  resistance  curve 

ef 
II,   r  =  -  i  is  equal  but  opposite  to  the  slope  of  the  arc  char- 

de 
acteristic  I,  —  ;  that  is,  at  the  stability  limit, 

ii+r=°->      ;        <*> 

and,  substituting  equation  (2)  in  (4),  gives 


and  the  total  voltage  consumed  by  the  arc  of  current  i  and 
length  I  and  the  series  resistance  r  required  to  just  reach  sta- 
bility is 

E  =  e  +  ir, 


,  fe  (*  +  Z.)  ,  *  (Z  +  Z.)  . 

—  eo  ~r  -      — ; r  -       — 7: — , 

\/i  2  Vt 


that  is, 


/.  VTV 

or,  E^e+ti.  (6) 

This  curve  is  called  the  stability  curve  of  the  arc.  It  is  shown 
as  IV  in  Fig.  48.  It  is  of  the  same  form  as  the  arc  characteristic 
I,  and  derived  therefrom  by  adding  50  per  cent  of  the  voltage 
consumed  in  the  arc  stream. 

Thus,  in  an  arc  requiring  80  volts,  of  which  e0  =  30  volts  are 
consumed  at  the  terminals,  ^  =  50  volts  in  the  arc  stream, 

for  stable  operation,  a  supply  voltage  of  more  than  E  =  e  +  -^ 
=  80  +  25  =  105  volts  is  required. 


ARC  LAMPS  AND  ARC  LIGHTING.  145 

The  stability  limit,  on  constant  potential,  thus  lies  at  an  ex- 
cess of  the  supply  voltage  over  the  arc  voltage  by  50  per  cent  of 
the  voltage,  ev  consumed  in  the  arc  stream.  In  general,  to  get 
reasonable  steadiness  of  the  current,  and  absence  of  drifting,  a 
supply  voltage  is  used  which  exceeds  the  arc  voltage  by  from 
75  per  cent  to  100  per  cent  or  more  of  the  voltage,  ev  of  the  arc 
stream. 

65.  The  preceding  consideration  applies  only  to  those  arcs 
in  which  the  gas  pressure  in  the  space  surrounding  the  arc,  and 
thereby  the  arc  vapor  pressure  and  temperature,  are  constant 
and  independent  of  the  current,  as  is  the  case  with  arcs  in  air 
(even  "  enclosed"  arcs,  as  the  enclosure  cannot  be  absolutely  air- 
tight), as  it  is  based  on  the  assumption  that  the  section  of  the 
vapor  stream  is  proportional  to  the  current.  With  arcs  in 
which  the  vapor  pressure  and  temperature  vary  with  the  current, 
as  with  vacuum  arcs,  as  the  mercury  arc,  the  reasoning  has  to  be 
correspondingly  modified.  Thus  in  the  mercury  arc  in  a  glass 
tube,  if  the  current  is  sufficiently  large  to  fill  the  entire  tube,  and 
not  so  large  that  condensation  of  the  mercury  vapor  cannot 
freely  occur  in  the  condensing  chamber,  the  power  pl  dissi- 
pated by  radiation,  etc.,  may  be  assumed  as  proportional  to  the 
length  Z  of  the  tube,  and  to  the  current  i: 

pi  =  6li  =  kli,  (7) 

thus  gives  e1  =  klf  or  independent  of  the  current;  and 

e  =  e0  +  ev 
=  e0  +  A*;  (8) 

that  is,  the  voltage  consumed  by  a  mercury  arc,  within  a  cer- 
tain range  of  current,  is  constant  and  independent  of  the  cur- 
rent, and  consists  of  a  constant  part,  the  terminal  drop  e0,  and 
a  part  which  is  proportional  to  the  length  and  to  the  diameter 
of  the  tube. 
Approximately  it  is  for  the  mercury  arc  in  a  vacuum: 

1.4 

e0  =  13  volts  ;  k  =  -y- 
Id 

hence,  , 


Calculating  approximately  the  increase  of  vapor  pressure  and 
thereby  of    arc-stream   resistance   at    high  currents,  and  the 


146  RADIATION,  LIGHT,  AND  ILLUMINATION. 

increase  of  resistance  at  low  current,  due  to  the  arc  stream  not 
completely  rilling  the  vapor  tube,  gives  for  the  vacuum  arc  the 
approximate  equation: 

I 
e  =  e«  + df°> 

7  7    •  d 

ald  -01 r- 

^ 

where 

ld  =  diameter  of  arc  tube,  cm., 
I  =  length  of  arc,  cm., 
i  =  current. 
For  the  mercury  arc,  it  is : 

e0  =  13  volts, 

a  =  1.68, 

6  =  0.29  for  mercury  anode, 

=  0.167  for  graphite  or  metal  anode, 

c  =  0.52. 

Arc  Length  and  Efficiency. 

66.  The  arc  most  frequently  employed  for  illumination  is 
the  plain  carbon  arc.  In  this  the  arc  flame  of  the  vapor  stream 
gives  no  useful  light,  but  the  light  is  given  by  the  black-body 
radiation  of  the  incandescent  carbon  terminal,  mainly  the 
positive  terminal,  which  is  hottest,  and  is  given  at  high  efficiency 
due  to  the  very  high  temperature  of  the  radiator.  The  light 
of  the  carbon  arc  thus  is  incandescent  light,  and  not  lumines- 
cence. In  the  alternating  carbon  arc,  alternately,  the  two  ter- 
minals are  positive  and  negative,  and,  as  relatively  little  heat  is 
produced  at  the  negative  terminal,  the  average  temperature  of 
the  carbon  terminals  of  an  alternating  arc  is  lower,  and  the 
efficiency  of  light  production  therefore  less.  Thus,  while  direct- 
current  carbon  arcs  reach  efficiencies  corresponding  to  specific 
consumptions  of  from  1  to  1.5  watts  per  mean  spherical  candle 
power,  alternating  carbon  arcs  show  only  from  2.5  to  3  watts 
per  candle  power,  or  even  still  higher  specific  consumption. 
Thus,  the  only  excuse  for  the  use  of  the  alternating  carbon  arc 
is  the  much  greater  simplicity  and  convenience  of  the  electric 
generating  apparatus,  the  stationary  transformer,  compared  to 
the  arc  machine  with  the  direct-current  arc,  and  with  the  de- 
velopment of  the  constant-current  mercury-arc  rectifier;  this 


ARC  LAMPS  AND  ARC  LIGHTING. 


147 


difference  in  the  simplicity  of  generation  of  the  arc  current  has 
largely  disappeared. 

In  the  direct-current  carbon  arc,  the  light  comes  mainly  from 
the  positive  terminal;  in  the  alternating  carbon  arc  equally 
from  both  terminals,  and  the  distribution  curve  of  the  light 
thus  is  different. 

Since  in  the  carbon  arc  no  useful  light  comes  from  the  arc 
flame,  the  voltage  and  therefore  the  power  consumed  in  the 
arc  flame  is  wasted,  and  in  general,  therefore,  the  efficiency  of 
light  production  of  the  carbon  arc  is  the  higher  the  shorter  the 
arc.  Thus  comparing  in  Fig.  49  a  1-in.  carbon  arc  A  with  a 


FIG.  49. 

0.5-in.  carbon  arc  B,  the  former  requires,  at  5  amperes,  112 
volts  and  560  watts,  the  latter  only  84  volts  and  420  watts, 
but  radiates  the  same  amount  of  light  from  the  incandescent 
tip  of  the  positive  carbon.  As  the  1-in.  arc  requires  33  per 
cent  more  power,  and  only  produces  the  same  amount  of  light, 
it  is  less  efficient  than  the  latter.  Thus,  the  shorter  we  make 
the  arc  and  the  less  power  we  therefore  consume  in  it  the  more 
efficient  seems  the  light  production,  as  we  produce  the  same 
amount  of  light  radiation  from  the  positive  terminal  in  either 
case.  When  we  come  to  short  arc  lengths,  however,  while  the 
same  amount  of  light  is  produced  at  the  positive  terminal,  we 
do  not  get  the  same  amount  of  light  from  the  lamp,  as  an 
increasing  part  of  the  light  is  intercepted  by  the  negative  ter- 
minal. Thus  with  the  1-in.  arc,  A,  in  Fig.  49,  the  light  escapes 


148  RADIATION,  LIGHT,  AND  ILLUMINATION. 

freely  from  the  incandescent  positive  only  in  the  space  above 
the  lines  m,  while  at  m  the  shadow  of  the  negative  terminal 
begins  to  obstruct  the  light  more  and  more,  and  does  so  com- 
pletely vertically  below  the  arc.  In  the  0.5-in.  arc  B  the  area 
covered  by  the  shadow  of  the  negative  terminals  is  somewhat 
increased,  but  in  both  arcs  A  and  B  the  obstruction  of  the 
light  by  the  shadow  of  the  negative  is  still  so  small  that  the 
saving  in  power  far  more  than  makes  up  for  it.  In  the  0.125-in. 
arc,  however,  C  in  Fig.  49,  the  shadow  of  the  negative  ter- 
minal m  has  crept  up  greatly,  and  thus,  when  decreasing  the 
arc  length,  a  point  is  reached  where  the  increasing  shadow 
of  the  negative  terminal  reduces  the  light  more  than  the  de- 
creasing arc  length  reduces  the  power  supply.  Maximum 
efficiency  of  light  production  thus  is  reached  in  the  carbon  arc 
at  a  certain  definite  arc  length  (which  depends  on  the  size  of 
the  electrodes  and  on  the  current),  at  which  the  change  of 
power  consumption  just  balances  the  change  of  radiated  light, 
which  results  from  a  change  of  arc  length  and  thereby  of 
shadow  of  negative  terminal. 

With  the  high-current  (9  to  10  amperes)  open  arcs,  the  maxi- 
mum efficiency  point  is  at  about  J-in.  arc  length,  giving  a 
voltage  consumption  of  about  45  to  50  volts.  Such  arcs  require 
daily  trimming,  and  therefore  are  no  longer  used  in  American 
cities,  except  in  a  few  places. 

The  open  or  short-burning  arc  has  been  practically  entirely 
superseded  by  the  enclosed  or  long-burning  arc  lamp,  in  which 
the  arc  is  enclosed  by  an  almost  air-tight  globe,  the  combustion 
of  carbon  is  greatly  decreased,  and  the  life  of  the  carbons  thus 
increased  about  tenfold. 

In  the  open  arc  of  large  current,  the  carbon  terminals  burn 
off  into  a  rounded  shape,  but  in  the  enclosed  arc,  the  current 
being  less  and  combustion  greatly  reduced,  the  carbon  terminals 
burn  off  to  more  flat  shape,  and  thus  obstruct  the  light  more; 
and,  furthermore,  since  at  the  lower  current  the  size  of  the 
incandescent  spot  of  the  positive  terminal  is  less,  the  maximum 
efficiency  of  light  production  in  the  enclosed  arc  lamp  is  reached 
at  a  much  greater  arc  length,  about  f  in.  As  the  result 
thereof,  the  enclosed  arc  lamp,  with  5,  6.5  or  7.5  amperes  in 
the  arc,  consumes  from  70  to  75  volts. 

67.   Entirely  different  are  the  conditions  in  the  luminous 


ARC  LAMPS  AND  ARC  LIGHTING.  149 

arc,  as  the  magnetite  arc.  In  this,  the  light  is  given  by  the 
vapor  stream,  and  not  by  the  terminals,  and  the  voltage  e0 
and  power  consumed  by  the  terminal  drop  thus  is  wasted,  and 
the  voltage  el  and  power  pt  consumed  by  the  arc  stream  is 
useful  for  light  production.  The  greater,  therefore,  the  voltage 
el  of  the  arc  stream  is,  compared  with  the  terminal  drop  e0,  or  in 
other  words  the  longer  the  arc,  the  higher  is  the  efficiency  of 
light  production.  Thus  a  4-amp.  magnetite  arc  of  0.125-in. 
length  requires  41  volts,  while  a  0.5-in.  4-amp.  arc  requires  64 
volts ;  that  is,  only  56  per  cent  more  voltage  and  thus  power,  but 
gives  about  four  times  the  light.  A  1-in.  arc  requires  95  volts 
or  48  per  cent  more  power  than  the  0.5-in.  arc,  and  gives  twice 
the  light.  The  greater,  thus,  the  arc  length  of  the  luminous 
arc,  with  the  same  current,  the  higher  is  the  efficiency.  How- 
ever, at  the  same  current,  the  longer  the  arc,  the  greater  is  the 
power  consumption.  In  the  design  of  the  arc  lamp  the  power 
consumption  is  given,  and  the  problem  is  to  select  the  most 
efficient  arc  length  for  a  given  and  constant  power  consumption. 
As  an  increase  of  arc  length  increases  the  arc  voltage  for  the 
same  power  consumption,  the  current  has  to  be  decreased,  and 
the  efficiency  of  the  arc  conductor  decreases  with  decrease  of 
current.  Thus,  with  increasing  arc  length  at  constant  power 
consumption  in  the  luminous  arc,  a  point  is  reached  where  the 
decrease  of  current  required  by  the  increase  of  arc  length  and 
thus  arc  voltage  decreases  the  efficiency  more  than  the  increase 
of  arc  length  increases  it.  Thus  with  the  luminous  arc,  for 
a  given  power  consumption,  a  definite  arc  length  exists,  which 
gives  maximum  efficiency. 

Assuming  the  light  given  by  the  arc  to  be  proportional  to  the 
arc  length  and  the  current  in  the  arc, 

L  =  k'li,  (9) 

if  the  power  p  shall  be  consumed  in  the  arc, 

ei  =  p]  (10) 

however,  by  (2), 

e=e0  +  ^  (11) 

Vi 

(neglecting  the  small  quantity  lv  as  the  calculation  can  obviously 
be  approximate  only). 


150  RADIATION,  LIGHT,  AND  ILLUMINATION. 

From  (10)  and  (11)  follows: 

~ (12) 


fe 

and,  substituting  this  in  (9),  gives: 

k 

L  =  -  (pVi  -  ejVi),  (13) 

and  the  maximum  amount  of   light  produced  by  power  p  is 
given  by:  dL 

This  gives 

(14) 


3e0 
hence,  by  (13):  0  z, 

(15) 

and  herefrom,  by  (12)  and  (11),  the  values  of  the  arc  length  Z 
and  the  arc  voltage  e. 

Assuming  p  =  300  watts,  and  the  constants  of  the  magnetite 
arc:  eQ  =  30,  k  =  31,  gives: 

i  =  3.33  amperes, 
e  =  90  volts, 
I  =  2.21  cm.  =  0.885  in. 

Near  the  maximum  efficiency,  where  the  efficiency  curve  is 
horizontal,  the  efficiency  does  not  vary  much  for  moderate 
changes  of  current  and  of  arc  length.  Thus,  in  above  instance, 
practically  the  same  efficiency  is  reached  for  currents  from  3 
amperes  to  4  amperes. 

Larger  currents  and  shorter  arc  lengths,  however,  are  pref- 
erable in  an  arc  lamp. 

(1)  Because  the  shorter  and  thicker  arc  is  less  affected  by 
minor  air  currents,  etc.,  than  the  thin  long  arc,  hence,  is  steadier. 

(2)  The  shorter  arc  gives  lower  voltage,  and  this,  in  constant- 
current  arc  lighting,  permits  with  the  same  total  circuit  voltage 
the  use  of  more  arc  lamps  in  series. 

Thus  in  the  magnetite  arc  lamp  a  current  of  4  amp.  has  been 
chosen. 

i  =  4:  e  =  75  volts,  and  I  +  l^  =  0.73  in.,  or  about  f-in.  arc 
length. 


ARC  LAMPS  AND  ARC  LIGHTING.  151 

In  general,  obviously  the  maximum  efficiency  points  of  lumi- 
nous arcs  occur  at  much  greater  arc  lengths  than  in  the  plain 
carbon  arc. 

Since  the  lower  efficiency  of  the  alternating  carbon  arc  is  due 
to  the  lower  temperature  of  the  terminals,  which  are  heated 
during  one  half-wave  only,  and  in  the  luminous  arc  the  tem- 
perature of  the  terminals  does  not  determine  the  light  pro- 
duction, but  the  light  is  produced  by  the  vapor  stream,  no 
essential  difference  exists  in  the  efficiency  of  a  luminous  arc, 
and  practically  no  difference  in  the  efficiency  of  the  flame- 
carbon  arc,  whether  operated  on  alternating  or  on  direct  current; 
that  is,  the  alternating  luminous  or  flame-carbon  arc,  with  the 
same  luminescent  material,  has  the  same  efficiency  as  the  direct- 
current  luminous  or  flame-carbon  arc,  but  the  alternating  plain 
carbon  arc  is  much  less  efficient  than  the  direct-current  carbon 
arc. 

Arc  Lamps. 

68.  The  apparatus  designed  for  the  industrial  production  of 
light  by  arc  conduction,  or  the  arc  lamp,  in  general  comprises 
four  elements : 

(1)  The  current-limiting  or  steadying  device. 

(2)  The  starting  device. 

(3)  The  feeding  device. 

(4)  The  shunt  protective  device. 

(1)  From  the  volt-ampere  characteristic  of  the  arc  as  given 
by  equation  (2)  and  curves,  Fig.  46,  it  follows  that  an  arc  can- 
not be  operated  directly  on  constant  voltage  supply,  but  in 
series  thereto  a  steadying  device  must  be  inserted;  that  is,  a 
device  in  which  the  voltage  increases  with  the  current  so  that 
the  total  voltage  consumed  by  the  arc  and  the  steadying  device 
increases  with  increase  of  current,  and  pulsations  of  current 
thus  limit  themselves. 

All  arc  lamps  for  use  on  constant  voltage  supply  thus  contain 
a  sufficiently  high  steadying  resistance,  or,  in  alternating-current 
circuits,  a  steadying  reactance. 

Arc  lamps  for  use  on  constant-current  circuits,  that  is,  cir- 
cuits in  which  the  current  is  kept  constant  by  the  source  of 
power  supply,  as  the  constant-current  transformer  or  the  arc 
machine,  require  no  steadying  resistance  or  reactance. 


152  RADIATION,  LIGHT,  AND  ILLUMINATION. 

Where  several  lamps  are  operated  in  series  on  constant  poten- 
tial mains,  as  two  flame-carbon  arcs  in  series  in  a  110-volt  cir- 
cuit, or  five  enclosed  arc  lamps  in  a  550-volt  railway  circuit, 
either  each  lamp  may  have  its  own  steadying  resistance,  or  a 
single  steadying  resistance  or  reactance  of  sufficient  size  may 
be  used  for  all  lamps  which  are  in  series  on  the  constant  poten- 
tial mains. 

(2)  Since  the  arc  does  not  start  itself,  but  has  to  be  started 
by  forming  the  conducting  vapor  bridge  between  the  terminals, 
all  arc  lamps  must  have  a  starting  device.     This  consists  of  a 
mechanism  which  brings  the  terminals  into  contact  with  each 
other  and  then  separates  them,  and  hereby  forms  the  vapor 
conductor,  that  is,  starts  the  arc. 

(3)  As  the  arc  terminals  consume  very  rapidly  in  some  arcs, 
as  the  open  carbon  arc,  and   very  slowly  in  others,  as  the 
enclosed  carbon  arcs  or  the  luminous  arcs,   some  mechanism 
must    be  provided  which  moves  the  terminals  towards   each 
other  at  the  rate  at  which  they  are  consumed,  and  thereby  main- 
tains constant  arc  length  and  thus  constant  voltage  and  power 
consumption. 

With  arcs  in  which  the  electrodes  consume  very  slowly,  as 
the  magnetite  arc,  the  feeding  may  occur  only  at  long  intervals, 
every  quarter  or  half  hour,  or  even  less  frequently,  while  in  arcs 
with  rapidly  consuming  electrodes,  as  the  flame  arcs,  practically 
continuous  feeding  is  required. 

(4)  The  circuit  between  the  arc  electrodes  may  accidentally 
open,  as  by  a  breakage  of  one  electrode,  or  by  the  consumption 
of  the  electrodes  if  the  lamp-trimmer  has  forgotten  to  replace 
them,  or  one  of  the  electrodes  may  stick  and  fail  to  feed,  and 
the  arc  thus  indefinitely  lengthen.     In  such  cases,  either  the 
entire  circuit  would  open,  and  thus  all  the  lamps  in  series  in 
this  circuit  go  out,  or,  if  the  circuit  voltage  is  sufficiently  high, 
as  in  a  constant-current  series  system,  the  arc  lamp  would  be 
consumed  and  the  circuit  damaged  by  a  destructive  arc.     Thus 
a  device  is  necessary  which  closes  a  shunt  circuit  between  the 
lamp  terminals  in  case  the  lamp  voltage  becomes  excessive  by 
a  failure  of  proper  operation  of  the  lamp. 

Where  only  one  lamp  is  operated,  on  constant  potential  low- 
voltage  supply,  no  such  protective  device  is  needed.  If  with 
two  or  more  lamps  in  series  on  constant  potential  supply,  no 


ARC  LAMPS  AND  ARC  LIGHTING.  153 

objection  exists,  in  case  of  the  failure  of  one  lamp,  to  have  the 
others  go  out  also,  the  shunt  protective  device  may  also  be 
omitted,  except  if  the  circuit  voltage  is  so  high  that  it  may 
damage  the  inoperative  lamp,  as  is  the  case  with  550  volts. 

When  operating  a  number  of  lamps  in  series  on  constant 
potential  supply,  as  two  flame  lamps  on  110  volts,  the  shunt 
circuit,  which  is  closed  in  case  of  the  failure  of  one  lamp  to 
operate,  must  have  such  a  resistance,  or  reactance  with  alter- 
nating currents,  that  the  remaining  lamp  still  receives  its 
proper  voltage,  even  if  the  other  lamp  fails  and  its  shunt  circuit 
closes.  With  alternating-current  lamps,  this  does  not  require  a 
reactance  of  such  size  that  the  potential  difference  across  the 
reactance  equals  that  across  the  lamp,  which  it  replaces,  but 
the  reactance  must  be  larger;  that  is,  give  a  higher  potential 
difference  at  its  terminals,  than  the  lamp  which  it  replaces,  to 
leave  the  normal  operating  voltage  for  the  remaining  lamp, 
since  the  voltage  consumed  by  the  reactance  is  out  of  phase 
with  the  voltage  consumed  by  the  lamp. 

69.  For  illustration,  the  operating  mechanism  of  a  constant 
direct-current  arc  lamp  is  shown  diagrammatically  in  Fig.  50 : 

The  lower  electrode  A  is  held  in  fixed  position.  The  upper 
electrode  B  slides  loose  in  a  holder  C,  and  thus,  if  there  is  no 
current  through  the  lamp,  drops  down  into  contact  with  the 
lower  carbon,  as  shown  in  Fig.  50.  When  there  is  a  current 
through  the  arc  circuit,  its  path  is  from  terminal  1  through 
electromagnet  S,  holder  C,  upper  electrode  B,  lower  electrode  A 
to  terminal  2.  The  electromagnet  S  is  designed  so  as  to  give  a 
long  stroke.  When  energized  by  the  current,  it  pulls  up  its 
armature,  the  lever  DD',  which  is  pivoted  at  E.  Through  the 
rod  F,  the  lever  D  pulls  up  the  clutch  G.  This  clutch  and  its 
operation  are  shown  in  larger  scale  in  Fig.  51,  A  and  B',  it  con- 
sists of  a  metal  piece  G,  which  has  a  hole  somewhat  larger  than 
the  upper  electrode  B.  This  electrode  slides  freely  through  the 
hole,  if  the  clutch  G  is  in  horizontal  position,  as  shown  in  Fig.  51a. 
When  the  rod  F  pulls  the  clutch  G  up,  and  thereby  inclines  the 
piece  G,  as  shown  in  Fig.  516,  the  edges  p  and  q  of  the  hole  in 
the  piece  G  catch  the  electrode  B,  and,  in  the  further  upward 
motion  of  D  and  F,  raise  the  other  electrode,  B,  from  contact 
with  the  lower  carbon,  A,  and  thereby  start  the  arc.  An  elec- 
tromagnet of  many  turns  of  fine  wire,  and  of  high  resistance,  P, 


154  RADIATION,  LIGHT,  AND  ILLUMINATION. 


FIG.  50. 


FIG.  51a. 


FIG.  51b. 


connected  in  shunt  between  the  lamp  terminals  1  and  2,  acts 
upon  the  side  D'  of  the  lever  DD',  opposite  from  the  side  D,  on 
which  the  series  magnet  S  acts.  With  the  carbons  in  contact 
with  each  other,  and  practically  no  voltage  between  the  lamp 
terminals  1  and  2,  the  coil  P  receives  no  current,  and  exerts  no 
pull.  When  by  the  action  of  the  series  magnet  S  the  lever  D 
pulls  up,  and  the  arc  starts  and  lengthens,  its  voltage  increases, 


ARC  LAMPS  AND  ARC  LIGHTING.  155 

a  branch  current  is  established  through  the  shunt  magnet  P, 
and  this  shunt  magnet  thus  opposes  the  series  magnet  S.  With 
increasing  arc  length  and  thus  arc  voltage,  a  point  is  reached, 
where  the  shunt  magnet  P  counterbalances  the  pull  of  the 
series  magnet  S,  and  the  lever  D  and  thereby  the  electrodes  B 
come  to  rest;  the  arc  has  reached  its  full  length,  that  is,  the 
starting  operation  is  over.  As  soon  as,  by  the  combustion  of 
the  electrodes,  the  arc  length  and  thereby  the  arc  voltage  be- 
gins to  rise,  the  current  in  the  shunt  magnet  P,  and  thus  its 
pull,  increases,  while  that  of  the  series  magnet  S,  being  ener- 
gized by  the  constant  main  current,  remains  constant;  the 
lever  D'  thus  pulls  up,  and  lowers  D,  and  thereby,  through  rod 
F  and  clutch  G,  the  upper  electrode  B,  and  thus  maintains  con- 
stant arc  length.  During  the  combustion  of  the  electrodes,  by 
the  operation  of  the  shunt  magnet  P  the  clutch  G  and  thereby 
the  upper  electrode  B  are  gradually  lowered,  and  the  arc  length 
thus  maintained  constant.  Ultimately,  however,  the  clutch  G 
hereby  approaches  the  horizontal  position,  shown  in  Fig.  51  A, 
so  far,  that  the  edges  of  the  hole,  p  and  q,  cease  to  engage,  and 
the  electrode  B  is  free  and  drops  down  on  the  lower  carbon  A. 
While  dropping,  however,  the  arc  shortens,  the  arc  voltage,  and 
thereby  the  current  in  the  shunt  magnet  P,  decreases,  the  pull 
of  this  magnet  decreases  correspondingly,  and  the  series  magnet 
S  pulls  the  clutch  G  up  again,  thereby  catches  the  electrode  B 
-usually  before  it  has  dropped  quite  down  into  contact  with 
the  lower  carbon  A  —  and  again  increases  the  arc  to  its  proper 
length,  and  the  same  cycle  of  operation  repeats:  a  gradual 
feeding  down  of  the  upper  electrode  B  by  the  shunt  magnet 
until  it  slips,  and  is  pulled  up  again  by  the  series  magnet  S. 

From  the  same  lever  D  is  supported,  by  rod  L,  a  contact- 
maker  K.  If  then  the  upper  electrode  B  should  stick,  and  thus 
does  not  slip,  when  by  the  shunt  magnet  P  the  clutch  G  has  been 
brought  into  horizontal  position,  or,  if  B  has  been  entirely  con- 
sumed, etc.,  the  arc  continues  to  lengthen  and  the  pull  of  the 
shunt  magnet  P  to  rise,  and  D  thereby  goes  still  further  down 
until  contact-maker  K  closes  the  contacts  MN,  and  thereby 
closes  a  shunt  circuit  from  terminal  1  over  resistance  R,  con- 
tacts MKN  to  terminal  2.  In  the  same  manner,  if,  by  the 
breaking  of  one  electrode  or  any  other  cause,  the  arc  should  be 
interrupted,  for  a  moment  the  full  current  passes  through  shunt 


156  RADIATION,  LIGHT,  AND  ILLUMINATION. 

magnet  P,  it  pulls  up  its  armature  D'  to  its  full  extent,  and 
thereby  closes  the  shunt  circuit  around  the  lamp. 

When  the  current  is  taken  off  the  circuit,  armature  D  drops 
down,  and  thereby  K  closes  the  shunt  circuit,  and  clutch  G 
releases  the  electrode  B,  and  it  drops  down  into  contact  with 
carbon  A.  In  starting  the  lamp,  two  paths  thus  are  available: 
over  series  magnet  S,  and  electrodes  B  and  A,  or  over  resistance 
R  and  contacts  MN.  While  the  resistance  of  the  former  path 
is  very  low,  it  is  not  entirely  negligible.  Therefore  a  sufficient 
resistance  R  must  be  inserted  in  the  by-path  MN,  so  that  in 
starting  practically  all  the  current  passes  over  S  and  the  elec- 
trodes, as  otherwise  the  lamp  would  not  start.  During  the 
pulling  up  of  the  armature  D  by  the  series  magnet  S,  in  start- 
ing, the  contact  K  opens,  before  the  clutch  G  has  caught  the 
electrode  B',  that  is,  while  the  electrodes  are  still  in  contact 
with  each  other,  and  the  opening  of  contact  K  therefore  breaks 
no  appreciable  voltage  or  current,  hence  is  sparkless. 

In  this  lamp,  no  steadying  resistance  is  used,  as  it  is  intended 
for  operation  on  a  constant-current  circuit.  If  used  on  con- 
stant-potential circuit,  as,  for  instance,  a  number  in  series  on 
550  volts,  a  steadying  resistance  R0  would  be  inserted,  as  indi- 
cated at  R0  in  Fig.  50. 

The  starting  of  the  arc  is  accomplished  by  series  magnet  S 
and  clutch  G;  the  feeding  by  shunt  magnet  P;  the  protective 
device  is  the  contact  MKN. 

Such  an  arc  lamp  is  called  a  differential  lamp,  as  it  is  con- 
trolled by  the  differential  action  of  a  shunt  and  a  series 
magnet. 

It  contains  a  floating  system  of  control;  that  is,  the  upper 
electrode  is  suspended  by  the  balance  of  two  forces,  exerted  by 
the  series  and  the  shunt  magnet;  that  is,  by  the  current  and 
the  voltage;  the  upper  carbon  therefore  is  almost  continuously 
moving  slightly  in  following  the  pulsation  of  the  arc  resistance 
which  occurs  during  operation.  Since,  with  the  plain  carbon 
arc,  the  arc  flame  gives  no  light,  this  pulsation  of  the  arc  length 
is  not  objectionable;  and,  since  the  lamp  regulates  very  closely 
and  rapidly  for  constant  terminal  voltage,  it  is  very  easy  on  the 
circuit,  that  is,  does  not  tend  to  produce  surging  of  current  and 
voltage  in  the  circuit.  The  floating  system  of  control  is,  there- 
fore, used  in  all  carbon  arc  lamps. 


ARC  LAMPS  AND  ARC  LIGHTING. 


157 


Where  a  single  lamp  is  operated  on  a  constant-potential 
circuit,  the  mechanism  can  be  simplified  by  omitting  the  pro- 
tective shunt  circuit  RMN,  and  omitting  the  shunt  magnet  P, 
as,  with  a  change  of  arc  length,  the  main  current  and  thereby 
the  pull  of  the  series  magnet  S  varies,  and  the  control  thus  can 
be  done  by  the  series  magnet.  Such  a  lamp  then  is  called  a 
series  lamp.  An  alternating-current 
series  lamp  is  shown  diagrammatically 
in  Fig.  52. 

In  starting,  the  series  magnet  S  pulls 
up  the  electrode  B  by  the  clutch  G, 
in  the  same  manner  as  in  Fig.  50. 
With  increasing  arc  length  and  thus 
increasing  voltage  consumed  by  the 
arc,  the  current  in  the  arc  and  thus 
in  the  series  magnet  S  decreases,  and 
thereby  the  pull  of  this  magnet,  until 
it  just  counterbalances  the  weight  of 
the  armature,  and  the  motion  stop. 
With  the  consumption  of  the  carbons, 
the  armature  D,  clutch  G  and  elec- 
trode B  gradually  move  down,  until 
the  clutch  lets  the  carbon  slip,  the 
arc  shortens,  the  current  rises,  and 
the  magnet  S  pulls  up  again,  the  same 
as  in  Fig.  50.  A  reactance  x  in  series 
with  the  lamp,  as  steadying  device, 
limits  the  current.  This  reactance 
usually  is  arranged  with  different  terminals,  so  that  more  or 
less  reactance  can  be  connected  into  circuit,  and  the  lamp 
thereby  operated,  with  the  same  arc  voltage,  on  supply  circuits 
of  different  voltage,  usually  from  110  to  125  volts. 

Obviously,  such  a  series  lamp  can  be  used  only  as  single 
lamp  on  constant  potential  supply,  as  it  regulates  by  the  varia- 
tion of  current,  and,  with  several  lamps  in  series,  the  current 
would  vary  in  the  same  manner  in  all  lamps.  One  lamp  would 
then  take  all  the  voltage,  draw  an  arc  of  destructive  length, 
while  the  other  lamps  would  drop  their  electrodes  together  and 
go  out. 

70.   With  the  luminous  arc,  in  which  the  light  is  proportional 


FIG.  52. 


158 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


to  the  arc  length,  pulsations  of  the  arc  length,  if  appreciable, 
give  pulsations  of  the  light,  and  the  floating  system  of  control, 
which  maintains  constant  voltage  by  varying  the  arc  length  in 
correspondence  with  the  pulsation  of  arc  resistance,  thus  is 
undesirable,  and  a  mechanism  maintaining  fixed  arc  length 
is  required.  Such  a  mechanism,  that  of  the  magnetite  arc  lamp, 

is  diagrammatically  illustrated 
in  Fig.  53. 

As,  during  operation,  a 
melted  pool  forms  on  the  sur- 
face of  the  electrode,  the  elec- 
trodes are  left  separated  from 
each  other  when  taking  the 
power  off  the  circuit,  since 
when  letting  them  drop  to- 
gether when  taking  off  the 
power  —  as  in  the  carbon  arc 
—  they  may  weld  together  and 
the  lamp  thus  fail  to  start 
again. 

A  represents  the  lower  or 
negative  magnetite  terminal 
which  is  movable,  B,  the  non- 
consuming  upper  positive  elec- 
trode, consisting  of  a  piece  of 
copper,  with  heat-radiating 
wings,  W,  which  is  a  station- 
ary and  fixed  part  of  the  lamp. 
C  is  the  chimney  required  to 
FlG-  53-  carry  off  the  smoke. 

When  starting,  the  circuit,  beginning  at  terminal  1,  passes 
contacts  MN,  through  a  powerful  electromagnet  or  solenoid  0 
and  resistance  R,  to  terminal  2.  The  solenoid  0  pulls  up  its 
core  D,  and  by  the  clutch  G  raises  the  lower  electrode  A  into 
contact  with  the  upper  electrode,  B,  and  thereby  closes  the 
circuit  from  1  over  series  coil  S,  electrodes  B  and  A,  to  terminal 
2.  The  series  coil  S  pulls  up  the  core,  and  thereby  opens  the 
contact  MN,  thus  cuts  out  the  shunt  circuit  OR.  The  solen- 
oid 0  thus  loses  its  excitation,  and  drops  the  clutch  G,  and  the 
lower  terminal  A  drops  away  from  the  upper  terminal  B  by  a 


ARC  LAMPS  AND  ARC  LIGHTING. 


159 


distance  which  is  fixed  by  an  adjustable  clutch,  Q,  and  thus 
starts  an  arc  of  definite  length. 

When  during  the  consumption  of  this  electrode  A  the  arc 
length  and  thereby  the  arc  voltage  rises,  the  shunt  magnet  P 
increases  in  strength,  and  ultimately  pulls  the  core  F  away 
from  the  series  magnet  S,  closes  the  contact  MN  of  the  shunt 
circuit  OR,  and  thereby  energizes  the  solenoid  0.  This  again 
raises,  by  the  clutch  G,  the  lower  electrode  A  into  contact  with 
the  upper  electrode  B,  and  so  repeats  the  cycle  of  operation. 

If  the  arc  between  A  and  B  opens,  the  solenoid  S  loses  its 
excitation,  the  coil  F  drops  and  closes  the  contact  MN  of  the 
shunt  circuit  OR. 

If  the  arc  resistance  were  perfectly  constant,  such  a  mechan- 
ism would  not  operate  satisfactorily,  as  the  arc  would  have  to 
lengthen  considerably  to  have  the  shunt  coil  P  overpower  the 
series  coil  S  sufficiently  to  pull  the  core  F  down,  close  the  con- 
tact MN,  and  thereby  feed. 

The  resistance  of  an  arc,  and  thereby,  at  constant  length, 
its  voltage,  pulsates,  however,  continuously,  about  as  shown 
diagrammatically  in  Fig.  54,  that  is,  peaks  of  voltage  of  vari- 


isol 

110 

1005 


\r 


FIG.  54. 

ous  height  follow  each  other.  Thus  with  an  average  arc  volt- 
age of  75,  momentary  peaks  of  85  volts  will  probably  be  reached 
every  few  seconds,  peaks  of  100  volts  every  few  minutes,  of  110 
volts  every  half  hour.  Adjusting  the  shunt  magnet  P  so  as  to 
operate  at  105  volts,  a  voltage  peak  above  105,  which  causes 
the  lamp  to  feed,  would  be  reached  about  every  20  minutes. 
During  20  minutes,  however,  the  arc  length  does  not  appre- 


160  RADIATION,  LIGHT,  AND  ILLUMINATION. 

ciably  increase  by  the  consumption  of  the  electrode.  Due  to 
the  character  of  the  arc  as  a  pulsating  resistance,  such  a  con- 
trolling mechanism  thus  maintains  constant  arc  length  by  a 
potential  magnet  set  for  a  voltage  considerably  above  the  aver- 
age arc  voltage. 

Such  a  mechanism,  controlling  for  constant  arc  length,  does 
not  operate  for  constant  voltage  at  the  lamp  terminals,  but 
allows  the  pulsation  of  the  arc  resistance  to  appear  as  pulsation 
of  the  terminal  voltage.  In  a  constant-current  circuit,  with 
many  lamps  in  series,  these  voltage  pulsations  of  the  individual 
arcs  overlap  and  have  no  effect  on  the  circuit.  When  operating, 
however,  a  lamp  of  such  a  mechanism  on  a  low-voltage  constant 
potential  circuit,  a  highly  inductive  steadying  resistance  is  de- 
sirable, to  take  care  of  the  pulsations  of  arc  voltage. 

71.  The  open  or  short-burning  carbon  arcs  of  former  times  — 
which  have  survived  only  in  a  few  cities  — were  operated  on 
constant  direct-current  circuits  of  9.6  and  6.6  amp.  with  40  to 
45  volts  per  lamp. 

The  present  enclosed  or  long-burning  carbon  arcs  are  oper- 
ated on  constant-current  circuits  of  5  amp.  and  6.6  amp. 
direct  current,  or  of  6.5  and  7.5  amp.  alternating  current,  with 
about  72  volts  at  the  lamp  terminals.  They  are  operated  as 
single  lamps,  of  5  to  9  amp.  on  direct-  or  alternating-current 
constant  potential  circuits  of  110  to  125  volts,  or  two  lamps  in 
series  on  circuits  of  220  to  250  volts. 

The  flame-carbon  arcs,  as  short-burning  open  arcs,  are  usually 
operated  two  in  series  on  constant-potential  circuits  of  110  to 
125  volts,  or  four  in  series  on  circuits  of  220  to  250  volts,  with 
10  to  15  amp.  in  the  arc. 

The  luminous  arcs  are  operated  on  4-  and  6.6-amp.  constant 
direct-current  circuits  (magnetite  lamp),  with  75  volts  per 
lamp,  and  on  3-  and  4.5-amp.  constant  alternating-current  cir- 
cuits (titanium-carbide  arc),  with  80  volts  per  lamp. 

Arc  Circuits. 

72.  Arc  lamps  are  built  for,  and  operated  on,  constant-poten- 
tial supply,  and  on  constant-current  supply.     In  general,  the 
constant-potential  arc    lamp  is  less   efficient,  as  voltage  and 
thereby  power  is  consumed  in  the  steadying  resistance  which  is 
required  to  limit  the  current,  that  is,  to  give  an  approximate 


ARC  LAMPS  AND  ARC  LIGHTING.  161 

constant-current  effect,  as  discussed  above.  In  alternating- 
current  circuits,  reactance  may,  and  usually  is,  employed  in- 
stead of  the  steadying  resistance,  and  the  waste  of  power  thereby 
greatly  decreased.  Voltage,  however,  is  still  consumed  and  the 
power  factor  lowered. 

An  additional  waste  of  energy  generally  occurs  in  constant- 
potential  arc-lamp  circuits,  due  to  the  standard  distribution 
voltages  of  low-potential  circuits  being  higher  than  necessary 
for  the  operation  of  a  single  lamp,  but  too  low  for  the  operation 
of  two  lamps  in  series.  Thus  with  an  enclosed  5-amp.  carbon 
arc  lamp,  with  about  70  volts  at  the  arc,  a  supply  voltage  of 
95  to  100  volts  would  be  sufficiently  high  above  the  stability 
curve  of  the  arc  (Fig.  46)  to  give  steady  operation.  Distri- 
bution voltages,  however,  vary  between  110  to  130  volts,  and 
the  difference  thus  must  be  consumed  in  resistance,  giving  an 
additional  waste.  (Except  in  those  rare  cases,  where  as  steady- 
ing resistance  some  useful  devices,  as  incandescent  lamps,  can 
be  employed.)  With  an  enclosed  arc  lamp  on  a  125- volt  cir- 
cuit, only  36  volts,  or  29  per  cent,  are  usefully  employed  in 
heating  the  carbon  terminals  and  thereby  producing  the  light, 
while  the  remaining  71  per  cent  is  wasted  in  the  resistance 
and  in  the  non-luminous  arc  flame.  Somewhat  better  are  the 
conditions  when  operating  two  high-current  open  arcs,  as  two 
flame  lamps,  in  series  on  such  a  circuit.  However,  at  the  lower 
distribution  voltage,  as  110  volts,  the  supply  voltage  may  be 
already  so  close  to  the  stability  limit  of  the  arc  that  the  arcs 
are  not  as  steady  as  desirable. 

The  low-current,  long  luminous  arcs  of  electro-conduction,  as 
the  magnetite  arc,  can  in  general  be  operated  only  with  diffi- 
culty on  circuits  of  110  to  125  volts,  and  therefore  are,  for 
constant-potential  service,  frequently  designed  for  operation  as 
single  lamps  on  220  to  250  volts  supply,  with  extra  great  arc 
length. 

For  indoor  illumination,  constant-potential  arc  lamps  must 
obviously  be  used,  as  safety  does  not  permit  the  introduction 
of  the  high-voltage  series  arc  circuits  into  houses.  For  out- 
door illumination,  as  street  lighting,  in  the  United  States  the 
constant-current  arc  lamp  is,  with  the  exception  of  the  interior 
of  a  few  very  large  cities,  as  New  York,  used  exclusively,  due  to 
its  greater  efficiency,  and  the  greater  distance  to  which  the  cur- 


162  RADIATION,  LIGHT,  AND  ILLUMINATION. 

rent  can  be  sent  at  the  high  voltage  of  the  constant-current 
circuit.  In  American  towns  and  cities,  where  arc  lamps  are 
used  for  street  lighting,  practically  always  the  entire  city  up  to 
the  farthest  suburbs  is  lighted  by  arc  lamps,  and  frequently  arc 
lamps  installed  even  beyond  the  reach  of  the  high-potential 
primary  alternating-current  supply.  To  reach  such  distances 
with  low-voltage  constant-potential  supply,  is  impossible,  and 
thus  the  constant-current  series  system  becomes  necessary.  In 
European  cities,  where  a  prejudice  exists  against  high-voltage 
constant-current  circuits,  and  people  are  satisfied  to  have  arc 
lamps  only  in  the  interior  of  the  city,  and  leave  the  lighting  of 
the  suburbs  to  gas  lamps,  constant-potential  street  lighting  is 
generally  employed,  and  is  eminently  satisfactory  within  the 
limitations  with  which  European  cities  are  satisfied,  but  would 
be  impossible  in  the  average  American  city. 

Where  plain  carbon  arcs  are  used  in  American  cities  the 
enclosed  arc  lamp  is  exclusively  installed,  and  open  arc  lamps 
have  survived  only  in  a  few  exceptional  cases,  mainly  where 
political  reasons  have  not  yet  permitted  their  replacement  by 
modern  lamps.  The  lesser  attention  required  by  the  enclosed 
arc  lamp  —  weekly  trimming  instead  of  daily  with  the  open  arc 
lamp  — has  been  found  to  make  it  more  economical  than  the 
open  arc  lamp  of  old.  In  Europe,  where  labor  is  cheaper,  and 
the  daily  attention  not  considered  objectionable,  the  open  or 
short-burning  arc  lamp  has  maintained  its  hold,  and  the  en- 
closed arc  lamp  has  never  been  used  to  any  great  extent.  With 
the  development  of  the  flame  carbon,  the  flame  arc,  therefore, 
has  found  a  rapid  introduction  in  Europe,  while  in  the  United 
States  it  has  been  excluded  from  use  in  street  lighting,  due  to 
its  short-burning  feature,  which  requires  daily  trimming,  and  is 
used  only  for  decorative  purposes,  for  advertising,  etc.,  and  for 
low-grade  interior  lighting,  as  foundries,  etc. 

In  spite  of  the  lower  efficiency  of  the  alternating  carbon  arc, 
the  constant-current  circuits  used  for  arc  lighting  are  generally 
alternating,  due  to  the  greater  convenience  of  generation  of 
alternating  current,  and  constant  direct-current  arc  circuits 
used  only  where  the  city  or  the  electric  light  company  lays  stress 
on  the  efficiency  of  light  production. 

While  the  development  of  the  constant-current  mercury  arc 
rectifier  has  made  the  generation  of  constant  direct  current 


ARC  LAMPS  AND  ARC  LIGHTING.  163 

almost  as  simple  and  convenient  as  that  of  alternating  current, 
this  has  very  little  increased  the  use  of  the  direct-current  en- 
closed arc  lamp,  but  when  changing  to  direct  current  sup- 
ply, usually  the  arc  lamp  is  also  changed  to  the  luminous  arc, 
the  magnetite  lamp,  which  gives  more  light  and  consumes  less 
power. 

In  constant-current  arc  circuits,  usually  from  50  to  100 
lamps  are  operated  in  series  on  one  circuit,  with  circuit  volt- 
ages of  4000  to  8000  volts.  Seventy-five-lamp  circuits,  of  6000 
volts,  probably  are  the  most  common. 

73.  Constant  direct  current  was  produced  by  so-called  "arc 
machines"  or  "constant-current  generators."  Of  these  only 
the  Brush  machine  has  survived,  and  is  now  also  beginning  to 
disappear  before  the  mercury  arc  rectifier,  which  changes  the 
alternating  current  of  the  constant-current  transformer  to  direct 
current  without  requiring  moving  machinery. 

The  Brush  machine  in  its  principle  essentially  is  a  quarter- 
phase  constant-current  alternator  with  rectifying  commutator. 
An  alternator  of  low  armature  reaction  and  strong  magnetic 
field  regulates  for  constant  potential:  the  change  of  armature 
reaction,  resulting  from  a  change  of  load,  has  little  effect  on 
the  field  and  thereby  on  the  terminal  voltage,  if  the  armature 
reaction  is  low.  An  alternator  of  very  high  armature  reaction 
and  weak  field,  however,  regulates  for  constant  current:  if  the 
m.m.f.,  that  is,  the  ampere-turns  required  in  the  field  coil  to 
produce  the  magnetic  flux,  are  small  compared  with  the  field 
ampere-turns  required  to  take  care  of  the  armature  reaction, 
and  the  resultant  or  magnetism-producing  field  ampere-turns 
thus  the  small  difference  between  total  field  excitation  and 
armature  reaction,  a  moderate  increase  of  armature  current 
and  thereby  of  armature  reaction  makes  it  equal  to  the  field 
excitation,  and  leaves  no  ampere-turns  for  producing  the  mag- 
netism; that  is,  the  magnetic  flux  and  thereby  the  machine 
voltage  disappear.  Thus,  in  such  a  machine,  the  current  out- 
put at  constant  field  excitation  rises  very  little,  from  full  volt- 
age down  to  short  circuit,  or,  in  other  words,  the  machine 
regulates  for  approximately  constant  current.  Perfect  constant- 
current  regulation  is  produced  by  a  resistance  shunted  across  the 
field,  which  is  varied  by  an  electromagnet  in  the  machine  circuit, 
and  lowered  — that  is,  more  current  shunted  through  it,  and 


164          RADIATION,  LIGHT,  AND  ILLUMINATION. 

thereby  the  field  excitation  decreased  — if  the  machine  cur- 
rent tends  to  rise  by  a  decrease  of  the  required  circuit  voltage, 
and  inversely. 

The  constant-current  regulation  of  the  arc  machine  thus  is 
not  produced  by  its  so-called  "  regulator/'  but  approximate 
constant-current  regulation  is  inherent  in  the  machine  design, 
and  the  regulator  merely  makes  the  regulation  perfect. 

A  more  explicit  discussion  of  the  phenomena  in  the  arc 
machine,  and  especially  its  rectification,  is  given  in  Chapter  III 
of  Section  II  of  "Theory  and  Calculation  of  Transient  Electric 
Phenomena  and  Oscillations." 

In  alternating-current  circuits,  approximate  constant-current 
regulation  is  produced  by  a  large  reactance,  that  is,  by  self- 
induction,  in  the  circuit.  In  transformers,  the  self-induction  is 
the  stray  field,  or  the  leakage  flux  between  primary  coil  and 
secondary  coil.  In  the  constant-current  transformer,  which  is 
most  generally  used  for  constant  alternating-current  supply 
from  constant  alternating  voltage,  the  primary  turns  and  the 
secondary  turns  are  massed  together  so  as  to  give  a  high  mag- 
netic stray  flux  between  the  coils.  Such  a  transformer  of  high 
internal  self-induction,  or  high  stray  flux,  regulates  approxi- 
mately for  constant  current.  Perfect  constant-current  regula- 
tion is  produced  by  arranging  the  secondary  and  the  primary 
coils  movable  with  regard  to  each  other,  so  that,  when  low  cir- 
cuit voltage  is  required,  the  coils  move  apart,  and  the  stray 
flux,  that  is,  the  reactance,  increases,  and  inversely.  The 
motion  of  the  coils  is  made  automatic  by  balancing  the  magnetic 
repulsion  between  the  coils  by  a  counter- weight.  A  discussion 
of  the  constant-current  transformer  and  its  mode  of  operation 
is  given  in  "Theory  and  Calculation  of  Alternating  Current 
Phenomena,"  Fourth  Edition,  page  85. 

In  the  so-called  "constant-current  reactance,"  the  two  coils 
of  the  constant-current  transformer  are  wound  for  the  same 
current,  and  connected  in  opposition  with  each  other,  and  in 
series  to  the  arc  circuit  into  the  constant-potential  mains. 
With  the  coils  close  to  each  other,  the  reactance  is  a  minimum, 
and  it  is  a  maximum  with  the  coils  their  maximum  distance 
apart. 

The  constant-current  reactance  has  the  advantage  of  greater 
cheapness,  but  also  has  the  serious  disadvantage  that  it  connects 


ARC  LAMPS  AND  ARC  LIGHTING.  165 

all  the  arc  circuits  electrically  with  the  constant-potential  alter- 
nating-current system,  and  any  ground  in  an  arc  circuit  is  a 
ground  on  the  constant-potential  supply  system.  As  grounds 
are  more  liable  to  occur  in  arc  circuits,  the  constant-current 
reactance  is  therefore  very  little  used,  and  generally  the  con- 
stant-current transformer  preferred,  as  safer. 

In  the  constant  direct-current  mercury-arc  rectifier  system, 
the  constant-potential  alternating-current  supply  is  changed  to 
constant  alternating  current  by  a  constant-current  transformer, 
and  the  constant  alternating  current  then  changed  to  constant 
direct  current  by  the  mercury-arc  rectifier.  An  explicit  dis- 
cussion of  the  phenomena  of  the  constant-current  mercury  arc 
rectifier  is  given  in  Chapter  IV  of  Section  II  of  "  Theory  and 
Calculation  of  Transient  Electric  Phenomena  and  Oscillations." 

If  the  constant-current  arc  circuit  accidentally  opens,  with  a 
Brush  machine  as  source  of  supply,  the  voltage  practically 
vanishes,  as  the  machine  has  series  field  excitation,  and  thus 
loses  its  field  on  open  circuit.  The  constant-current  trans- 
former, however,  maintains  its  voltage,  and  gives  maximum 
voltage  on  open  circuit.  The  mercury  arc  rectifier,  when  sep- 
arately excited  by  a  small  exciting  transformer,  also  maintains 
its  voltage  on  open  circuit.  If,  however,  after  starting,  the 
excitation  is  taken  off,  that  is,  the  exciting  circuit  opened,  as 
is  permissible  in  a  steady  arc  circuit,  the  voltage  in  the  arc 
circuit  disappears  if  the  arc  circuit  is  opened.  Inversely,  when 
connecting  an  arc  circuit  to  a  Brush  arc  machine,  an  appre- 
ciable time  elapses  while  the  voltage  of  the  machine  builds 
up,  while  with  the  constant-current  transformer  and  thus  also 
with  the  constant-current  mercury  arc  rectifier  system,  full  volt- 
age exists  even  before  the  circuit  is  closed. 


LECTURE  IX. 
MEASUREMENT   OF    LIGHT   AND    RADIATION. 

74.  Since  radiation  is  energy,  it  can  be  measured  as  such 
by  converting  the  energy  of  radiation  into  some  other  form  of 
energy,  as,  for  instance,  into  heat,  and  measuring  the  latter. 

Thus  a  beam  of  radiation  may  be  measured  by  having  it 
impinge  on  one  contact  of  a  thermo-couple,  of  which  the  other 
contact  is  maintained  at  constant  temperature.  A  galvanom- 
eter in  the  circuit  of  this  thermo-couple  thus  measures  the 
voltage  produced  by  the  difference  of  temperature  of  the  two 
contacts  of  the  thermo-couple,  and  in  this  manner  the  temper- 
ature rise  produced  by  the  energy  of  the  incident  beam  of  radia- 
tion is  observed. 

Probably  the  most  sensitive  method  of  measuring  even  very 
small  amounts  of  radiation  is  the  bolometer.  The  beam  of 
the  radiation  (or  after  dissolving  the  beam  into  a  spectrum, 
the  wave  length  of  which  the  power  is  to  be  measured)  impinges 
upon  a  narrow  and  thin  strip  of  metal,  as  platinum,  and  thereby 
raises  its  temperature  by  conversion  of  the  radiation  energy 
into  heat.  A  rise  of  temperature,  however,  produces  a  rise  of 
electric  resistance,  and  the  latter  is  measured  by  enclosing  the 
platinum  strip  in  a  sensitive  Wheatstone  bridge.  The  rise  of 
temperature  of  the  platinum  strip  by  the  small  power  of  radia- 
tion obviously  is  so  small  that  it  could  not  be  observed  by 
any  thermometer.  Electric  resistance  measurements,  however, 
can  be  made  with  extreme  accuracy,  and  especially  extremely 
small  changes  of  resistance  can  be  measured.  Thus  a  change 
of  resistance  of  1  in  a  million  and,  with  very  sensitive  measure- 
ments, even  many  times  smaller  changes  can  be  observed.  As 
1  deg.  cent,  produces  a  resistance  change  of  about  0.4  per  cent, 
a  change  of  one  millionth  corresponds  to  a  temperature  rise 
°f  ?tfW  deg.  cent.  Thus,  by  the  bolometer,  extremely  small 
amounts  of  radiation  can  be  measured,  as,  for  instance,  the 
power  of  the  moon's  radiation,  etc. 

166 


MEASUREMENT  OF  LIGHT  AND  RADIATION.        167 

The  total  radiation  energy  of  a  body  for  a  given  time  can  be 
measured  by  absorbing  it  and  measuring  the  heat  produced  by 
it,  as;  for  instance,  the  amount  of  ice  melted  in  a  calorimeter. 
Any  particular  range  of  the  total  radiation,  as,  for  instance,  the 
total  visible  radiation,  can  be  measured  in  the  same  manner 
by  passing  the  radiation  first  through  a  body  which  absorbs 
that  part  which  is  not  desired,  for  instance,  a  body  transparent 
to  visible,  but  opaque  to  invisible  radiation.  As  no  body  is 
perfectly  transparent  to  one,  perfectly  opaque  to  another  radi- 
ation, the  separation  of  the  radiation  by  absorption  is  nec- 
essarily incomplete,  and  correction  must  therefore  be  made 
in  the  result.  This  makes  this  method  rather  inconvenient 
and  inaccurate.  Even  when  measuring  the  total  radiation  by 
absorption  in  a  calorimeter,  it  is  practically  impossible  to 
collect  the  total  radiation  without  either  losing  some,  or 
including  energy,  which  is  not  radiation,  but  heat  conduc- 
tion or  convection.  Obviously,  by  enclosing  the  radiator  in 
the  calorimeter,  the  latter  would  measure  not  only  the  radi- 
ation, but  also  the  power  lost  by  heat  conduction,  convec- 
tion, etc. 

Sometimes  the  power  of  radiation  can  be  measured  by  meas- 
uring input  and  losses.  Thus,  in  an  incandescent  lamp,  the 
electric-power  input  is  measured,  and  the  power  lost  by  heat 
conduction  and  convection  estimated  if  not  entirely  negligible. 
In  those  cases  in  which  all  or  most  of  the  energy  supplied  is 
converted  into  radiation,  as  in  an  incandescent  lamp,  this 
method  is  the  most  exact.  However,  it  can  directly  measure 
only  the  total  radiation  power.  To  measure  the  different  parts 
of  the  radiation  so  as  to  determine  separately  the  power  in  the 
visible,  the  ultra-red,  and  the  ultra-violet  range,  the  method  of 
input  and  losses  can  be  used  to  give  the  total  radiation  power, 
and,  by  bolometer  or  other  means,  the  relative  powers  of  the 
component  radiations  measured  in  a  beam  of  light.  From  the 
total  radiation  and  the  ratio  of  its  components,  then,  follows 
the  values  of  radiation  power  of  the  components. 

75.  Light,  however,  cannot  be  measured  by  any  of  the  pre- 
ceding methods,  since  light,  in  the  sense  in  which  it  is  con- 
sidered photometrically,  is  not  power,  but  is  the  physiological 
effect  of  certain  wave  lengths  of  radiation,  and  therefore  can- 
not be  measured,  physically,  as  power,  but  only  physiologically, 


168  RADIATION,  LIGHT,  AND  ILLUMINATION. 

by  comparison  with  other  physiological  effects  of  the  same 
nature. 

The  power  of  visible  radiation  obviously  can  be  measured, 
and  thus  we  can  express  the  power  of  the  visible  radiation  of 
a  mercury  lamp  or  an  incandescent  lamp  in  watts.  But  the 
power  of  visible  radiation  is  not  proportional  to  the  physiologi- 
cal effect,  and  thus  not  a  measure  thereof.  One  watt  of  green 
radiation  gives  many  times  as  great  a  physiological  effect,  that 
is,  more  light,  as  does  one  watt  of  red  or  violet  radiation,  and, 
besides,  gives  a  different  kind  of  physiological  effect:  a  differ- 
ent color. 

The  unit  in  which  illuminating  value  of  light,  or  its  intensity, 
is  expressed  as  the  "candle-power,"  is,  therefore,  a  physiological 
and  not  a  physical  quantity,  and  hence  it  has  no  direct  or  con- 
stant relation  to  the  unit  .of  power,  or  the  watt.  The  unit  of 
light  intensity  has  been  chosen  by  convention:  as  the  physio- 
logical effect  exerted  on  the  human  eye  by  5  sq.  mm.  of  melting 
platinum,  or  by  a  flame  burning  a  definite  chemical  compound 
—  as  amyl  acetate  or  pentane  —  at  a  definite  rate  and  under 
definite  conditions,  etc. 

Broadly,  therefore,  the  conception  of  a  chemical  equivalent  of 
light,  that  is,  a  relation  between  candle  power  and  watt,  is 
irrational,  just  as,  broadly,  a  relation  between  time  and  distance 
is  irrational;  that  is,  just  as  distance  cannot  be  expressed  by 
the  unit  of  time,  so  candle  power  cannot  be  expressed  by  a 
unit  of  power,  as  the  watt.  A  relation  between  two  such 
inherently  different  quantities  can  be  established  only  by  an 
additional  conventional  assumption,  and  varies  with  a  change 
of  this  extraneous  assumption.  Thus  stellar  distances  are 
measured  in  " light  years,"  that  is,  by  the  distance  traveled  by 
the  light  in  one  year,  as  unit.  So  also  the  physiological  effect 
of  one  definite  color  of  light,  as  that  of  the  green  mercury  line, 
or  the  yellow  sodium  line,  or  the  red  lithium  line,  can  be  related 
to  the  unit  of  power,  or  the  watt,  and  we  may  speak  of  a  me- 
chanical equivalent  of  green  light,  or  of  yellow  light,  or  of  red 
light.  When  doing  so,  however,  we  give  to  the  term  "  mechan- 
ical equivalent"  a  different  meaning  from  what  it  has  in  physics, 
for  instance,  as  "mechanical  equivalent  of  heat."  The  latter 
is  the  constant  relation  between  two  different  forms  of  the 
same  physical  quantity,  while,  for  instance,  the  "mechanical 


MEASUREMENT  OF  LIGHT  AND  RADIATION.        169 

equivalent  of  green  light "  is  the  relation  between  a  physiolog- 
ical effect  and  the  physical  quantity  required  to  produce  the 
effect,  and  thus  is  not  necessarily  constant,  but  may,  and  does, 
vary  with  the  intensity  of  the  effect,  the  individuality  of  the 
observer,  etc.  It  appears,  however,  that  at  higher  intensities 
the  relation  is  very  nearly  constant  and  the  same  with  differ- 
ent observers,  so  that  it  is  possible  to  express  the  physiological 
effect  of  a  definite  wave  length  of  radiation,  within  the  accuracy 
of  physiological  measurements,  by  the  power  consumed  in  pro- 
ducing this  wave  length  of  radiation;  but  it  becomes  entirely 
impossible  to  compare  physiological  effects  of  widely  different 
wave  lengths  by  comparing  the  power  required  to  produce  them. 

When  speaking  of  mechanical  equivalent  of  light,  it  thus 
must  be  understood  in  the  extended  meaning  of  the  word,  as 
discussed  above. 

76.  In  photometry,  and  in  general  in  illuminating  engineer- 
ing, it  is  of  essential  importance  to  keep  in  mind  this  difference 
in  the  character  of  light,  as  physiological  effect,  and  radiation, 
as  physical  quantity  of  power.  This  is  the  reason  why  all 
attempts  to  reduce  photometry  to  a  strictly  physical  measure- 
ment, and  thereby  bring  photometric  determinations  up  to 
the  high  grade  of  exactness  feasible  in  physical  observations, 
have  failed  and  must  necessarily  fail;  we  cannot  physically 
compare  an  effect  as  light,  which  is  not  a  physical  quantity, 
but  somewhere  in  all  photometric  methods  the  physiological 
feature,  that  is,  the  judgment  of  the  human  eye,  must  always 
enter. 

Photometric  tests  therefore  can  never  have  the  accuracy  of 
strictly  physical  determinations.  All  attempts  to  eliminate 
the  judgment  of  the  human  eye  from  photometry,  by  replac- 
ing it  by  the  selenium  cell,  or  the  photographic  plate,  or 
Crookes'  radiometer,  etc.,  necessarily  are  wrong  in  principle  and 
in  results:  some  of  those  instruments,  as  the  bolometer,  the 
radiometer,  etc.,  compare  the  power  of  the  radiation,  others, 
as  the  selenium  cell  or  the  photographic  plate,  the  power  of 
certain  changes  of  radiation,  but  their  results  are  comparisons 
of  power,  and  not  of  physiological  effects,  and  thus  they  can- 
not be  of  value  in  measurement  of  illuminating  power. 

Measurements  of  light  thus  are  made  by  comparison  with 
an  arbitrarily  chosen  conventional  unit,  a  primary  standard 


170  RADIATION,  LIGHT,  AND  ILLUMINATION. 

of  light,  as  " standard  candle,"  or  a  duplicate  or  multiplicate 
thereof.  Obviously,  in  measurements  of  light,  usually  not  the 
primary  standard  of  light  is  used,  but  a  more  conveniently 
arranged  secondary  standard  of  light,  that  is,  a  standard  which 
has  been  calibrated  by  comparison,  directly  or  indirectly,  with  a 
primary  standard. 

77.  The  most  accurate  method  of  comparing  lights  is  the 
zero  method,  as  represented  by  the  different  types  of  photom- 
eters. The  illumination  produced  by  the  two  different  sources 
of  light  —  the  one  to  be  tested  and  the  standard  —  are  made 
equal  by  changing  the  relative  distances  of  the  sources.  At  equal 
illumination  their  intensities  are  proportional  to  the  square  of 
their  distances.  Thus,  for  instance,  in  the  bunsen  photometer, 
as  shown  diagrammatically  in  its  simplest  form  in  Fig.  55,  the 


FIG.  55. 

two  white  screens  A  and  B  are  illuminated,  the  one,  A,  by  the 
light,  L,  which  is  to  be  tested,  the  other,  B,  by  the  standard  S, 
as  a  calibrated  or  standardized  16-cp.  incandescent  lamp,  and 
then  either  L  or  S  or  both  are  moved  until,  seen  from  (7,  the 
two  sides  A  and  B  of  the  screen  become  equal,  that  is,  the  divid- 
ing line  C  between  them  disappears.  When  this  is  the  case, 
L  -T-  S  =  x2  -T-  7/2,  where  x  and  y  are  the  two  distances  of  the 
sources  from  the  screen. 

Different  modifications  of  the  bunsen  photometer  are  most 
commonly  used. 

As  the  sensitivity  of  the  eye  to  differences  of  illumination  is 
not  very  great,  usually  a  number  of  readings  are  taken  on  the 
photometer,  and  then  averaged. 

For  testing  incandescent  lamps,  L,  as  standard  S,  a  calibrated 
incandescent  lamp  is  used,  operated  on  the  same  voltage  supply, 
so  that  fluctuations  of  light  caused  by  minor  fluctuations  of  sup- 
ply voltage  eliminate  by  appearing  in  both  sources  L  and  S. 


MEASUREMENT  OF  LIGHT  AND  RADIATION.        171 


For  similar  reasons,  when  testing  gas  lamps  or  other  flames, 
L,  as  S,  a  flame  standard,  as  the  pentane  lamp,  is  used,  so  that 
the  effect  of  barometric  pressure,  humidity  of  the  air,  etc., 
appears  in  both  lamps  and  thereby  does  not  appreciably  affect 
the  comparison  of  their  light. 

A  quick  and  approximate  method  of  comparison  of  sources 
of  light  is  given  by  the  shadow  photometer  by  moving  an 
object  between  the  two  lamps  until  the  two  shadows  of  the 
object  give  the  same  darkness.  When  this  is  the  case,  the 
illumination  at  the  object  is  the  same,  and  the  intensities  of 
the  two  sources  are  then  proportional  to  the  square  of  their  dis- 
tances from  the  object.  Street  lamps  can,  in  this  manner,  be 
rapidly  compared,  with  fair 
accuracy,  by  pacing  the 
distance  from  the  one  to 
the  other,  and  noting  when 
the  two  shadows  of  the 
observer  are  equal  in  dark- 
ness. If  then  at  x  steps 
from  the  one  lamp,  Llt  the 
shadows  are  equal,  and  y 
further  steps  are  required 
to  reach  the  second  lamp, 
L0,  it  is : 


0 


A  very  convenient  form 
of  photometer,  which  gives 
good  results  even  where 
the  two  lights  are  of  some- 
what different  color,  is  the  FlG  56 
paraffine  photometer.  A 

block  of  paraffine  is  cast,  as  shown  in  Fig.  56,  divided  by  a 
sheet  of  tinfoil  in  the  center  C,  and  covered  with  tinfoil  except 
at  the  top  and  on  the  sides  A  and  B.  It  is  advantageous  to 
have  the  center  sheet  of  tinfoil  C  perforated  by  a  hole  D. 

The  block  of  paraffine  then  is  held  so  that  the  side  A  is  illu- 
minated by  the  one  lamp,  L,  the  side  B  by  the  other  lamp,  S,  as 
shown  in  Fig.  57.  As  paraffine  is  translucent,  the  entire  block 
then  appears  luminous,  and  a  beam  of  light  is  seen  traversing 


172  RADIATION,  LIGHT,  AND  ILLUMINATION. 

the  block  from  the  hole  D,  on  the  side  which  receives  less  light. 
By  moving  the  paraffine  block  between  the  lamps  L  and  S, 
until  both  sides  of  it  are  of  the  same  luminosity,  that  is,  the 
dividing  line  C  and  the  beam  cast  by  hole  D  disappear,  equality 
of  the  two  illuminations  can  be  located  rapidly  and  with  great 
accuracy. 


FIG.  57. 

78.  When  comparing  lamps  giving  light  of  the  same  color,  as 
incandescent  lamps  of  the  same  filament  temperature,  that  is, 
the  same  efficiency,  exact  comparisons  can  be  made  —  within 
the  limits  of  sensitivity  of  the  eye  for  intensity  differences  — 
by  the  photometer  by  making  the  two  sides  A  and  B  of  the 
Bunsen  photometer  screen,  or  the  two  halves  of  the  paraffine 
block,  identical,  that  is,  making  the  dividing  line  C  disappear. 
If,  however,  the  color  of  the  two  lights  is  not  the  same,  as,  for 
instance,  when  comparing  a  tungsten  lamp  and  an  ordinary 
incandescent  lamp,  no  position  of  the  photometer  can  be  found 
where  the  dividing  line  C  between  A  and  B  (Figs.  55,  57)  dis- 
appears, but  a  color  difference  always  remains.  To  make  a 
comparison,  it  is  therefore  necessary  for  the  eye  to  judge 
when  the  two  sides  A  and  B  are  of  the  same  intensity  while  of 
different  colors.  If  the  color  difference  is  small,  as  between  two 
different  types  of  incandescent  lamps,  this  can  be  done  with 
fair  accuracy,  though  obviously  not  as  accurately  as  the  com- 
parison of  lights  of  identical  colors.  If,  however,  the  color 
difference  is  great,  as  between  the  mercury  arc  and  the  orange- 
yellow  carbon  filament  lamp,  the  uncertainty  of  equality  of 
the  intensity  of  illumination  becomes  very  great,  and  constant 
errors  appear,  due  to  the  difference  of  the  physiological  effect 
of  different  colors,  and  differences  also  appear  between  differ- 
ent observers,  so  that  the  photometric  comparison  of  light 
sources  of  greatly  different  colors  is  quite  unreliable,  and  that 
not  merely  by  inaccuracy,  but  by  unknown  and  individual  con- 
stant errors. 

In  such  cases,  frequently  lights  of  intermediary  color  are 
used  to  reduce  the  differences  in  each  observation.  Thus  the 
carbon  filament  lamp  is  compared  with  the  tungsten  lamp,  the 


MEASUREMENT  OF  LIGHT  AND  RADIATION.        173 

tungsten  lamp  with  the  carbon  arc  lamp,  and  the  latter  with 
the  mercury  arc  lamp.  Hereby  the  uncertainty  of  each  obser- 
vation is  reduced  by  the  reduced  color  difference.  In  the  final 
result,  however,  the  comparison  of  the  carbon  incandescent- 
lamp  standard  and  the  mercury  arc  lamp  no  advantage  is 
gained,  because  the  errors  of  the  successive  measurements  add. 
Especially  is  this  the  case  with  the  constant  errors,  that  is, 
errors  due  to  the  specific  color  effect,  and  in  consequence  thereof 
the  inaccuracy  of  the  final  result  is  not  much  better  than  it 
would  be  by  single  and  direct  comparison. 

A  photometer  which  is  sometimes  used  for  comparing  lights 
of  different  color,  and  is  based  on  a  different  principle  from 
either  of  the  above  discussed  instruments,  is  the  flicker  pho- 
tometer. In  its  simplest  form  it  consists  of  a  stationary  disk, 
illuminated  by  the  one  lamp,  and  a  rotating  half  disk  or  sector 
in  front  of  it,  which  is  illuminated  by  the  other  lamp.  At  slow 
rotation  a  flicker  shows,  which  disappears  if  the  speed  be- 
comes sufficiently  high.  It  is  obvious  that  the  more  nearly 
equal  the  effect  on  the  eye  of  the  two  illuminations  —  that  of  the 
stationary  disk  and  that  of  the  revolving  sector  —  the  lower  is 
the  speed  at  which  the  flicker  disappears,  and,  by  adjusting  the 
distances  of  the  two  lamps  so  as  to  cause  the  flicker  to  dis- 
appear at  the  minimum  speed,  the  instrument  indicates  equality 
of  the  effect  of  the  two  successive  illuminations  on  the  eye. 
This  is  frequently  considered  as  representing  equality  of  the 
illumination,  and  the  instrument  in  this  manner  used  to  com- 
pare illuminations.  There  is,  however,  no  reason  why  this 
should  be  the  case,  but,  on  the  contrary,  it  is  improbable.  As 
the  persistence  of  vision,  and  in  general  the  physiological  effects 
of  different  colors,  are  different,  the  flicker  photometer  must  be 
expected  to  have  a  constant  error  which  increases  with  color 
difference;  that  is,  it  does  not  compare  lights  of  different  color 
by  their  illuminating  values,  but  by  some  other  feature  not 
directly  related  thereto. 

79.  The  photometer  thus  cannot  satisfactorily  compare  lights 
of  different  colors.  After  all,  this  is  obvious:  the  photom- 
eter compares  by  identity,  but  lights  of  different  colors  can- 
not be  identical,  and  thus  two  such  lights  cannot  be  more 
broadly  compared  than  any  other  two  quantities  of  different 
character;  that  is,  a  green  light  can  no  more  be  equal  to  a  red 


174  RADIATION,  LIGHT,  AND  ILLUMINATION. 

light  than  a  piece  of  stone  can  be  equal  to  a  piece  of  ice.  A 
comparison  of  quantities  of  different  nature  is  possible  only 
regarding  particular  features  of  the  quantities  which  they  have 
in  common.  Thus  a  piece  of  stone  and  a  piece  of  ice  can  be 
compared  regarding  their  weight,  or  their  density,  etc.  In  the 
same  manner,  two  different  colors  of  light,  or  in  general  two 
different  frequencies  of  radiation,  can  be  compared  by  any 
feature  which  they  have  in  common.  Thus,  for  instance,  the 
photographic  plate  compares  them  in  their  chemical  activity, 
the  bolometer  by  their  physical  energy. 

Light  is  used  for  seeing  things  by,  that  is,  distinguishing 
objects  and  differences  between  objects.  Regarding  this  feature, 
the  distinction  of  objects  given  by  them,  different  colored  lights 
can  be  compared,  and  a  green  light  can  be  made  equal  to  a  red 
light  in  illuminating  value. 

It  thus  means  that  any  two  lights,  regardless  of  their  color, 
have  the  same  intensity  if,  at  the  same  distance  from  them, 
objects  can  be  seen  with  the  same  distinctiveness,  as,  for  in- 
stance, print  read  with  equal  ease.  The  only  method,  therefore, 
which  permits  comparing  and  measuring  lights  of  widely  differ- 
ent color  is  the  method  of  " reading  distances,"  as  used  in  the 
so-called  luminometer.  It  after  all  is  the  theoretically  correct 
method  of  comparison,  as  it  compares  the  lights  by  that  prop- 
erty for  which  they  are  used.  Curiously  enough,  the  lumi- 
nometer, although  it  has  the  reputation  of  being  crude  and 
unscientific,  thus  is  the  only  correct  light-measuring  instrument, 
and  the  photometer  correct  only  in  so  far  as  it  agrees  with  the 
luminometer,  but,  where  luminometer  and  photometer  disagree, 
the  photometer  is  wrong,  as  it  gives  a  comparison  which  is 
different  from  the  one  shown  by  the  lights  in  actual  use  for 
illumination. 

The  relation  between  luminometer  and  photometer  for  meas- 
uring light  intensity,  therefore,  is  in  a  way  similar  to  the  relation 
between  spark  gap  and  voltmeter  when  testing  the  disruptive 
strength  of  electrical  apparatus:  while  the  voltmeter  is  fre- 
quently used,  the  exact  measure  of  the  disruptive  strength  is 
the  spark  gap  and  not  the  voltmeter,  and,  where  the  spark  gap 
and  voltmeter  disagree,  the  voltmeter  must  be  corrected  by  the 
spark  gap.  In  the  same  manner  the  luminometer  measures 
the  quality  desired  —  the  illuminating  value  of  the  light  —  but 


MEASUREMENT  OF  LIGHT  AND  RADIATION.        175 


FIG.  58. 


the  photometer  may  be  used  as  far  as  it  agrees  with  the  lumi- 
nometer. 

80.  The  luminometer  can  hardly  be  called  an  instrument, 
but  it  is  merely  a  black  box,  as  shown  in  Fig.  58,  to  screen  off 
all  extraneous  light,  and 
allow  only  the  light  of  the 
source  which  is  to  be  ob- 
served, to  fall  on  the  print. 
The  print  obviously  must 
be  black  on  white,  that  is, 
complete  absorption  and 
complete  reflection,  so  as 
not  to  discriminate  in 
favor  of  particular  colors. 
No  great  accuracy  could 
be  reached  by  merely  com- 
paring the  ease  of  reading 
the  same  kind  of  print  with  different  sources  of  light.  A  high 
accuracy,  however,  is  reached  by  using  a  print  which  does  not 
give  definite  words  — in  which  letters  which  are  not  clearly 
seen  cannot  be  guessed  from  the  sense  of  the  word  or  sentence 
—  but  a  jumble  of  letters,  capitals  and  small  letters,  arranged  in 
meaningless  words. 
Such  a  luminometer  chart  is  given  below: 

Amhof  dirito  amritu,  Lisno  ladse  pemrane  odo  Ulay 
Foresca  1598720  woleb  noitaidar.  Ybod  ergy  may 
Pewos  ex  Idetnera,  bsor  poge  Morf  Tenscerophop  War- 
dog;  Omsk  whykow  efforau  tespo  ygnew  col  Brispo 
Monas  albo  darmosphor?  Cottef  vol  Demno  myo 
36802  Erbtomy,  quot  Hiaworu  pio  Nio  cuguab  Qaphla- 
qua  H  530  K  b  n  q;  267  Lloysir  baraka  nunc,  cinq 
Viamara  W  x  4  zoliaq  kama  nambosi  erianoscum. 
Zaraz  didym  fore  ik  yiquia  Fumne. 

With  such  a  printed  chart  in  the  luminometer,  the  observer 
moves  towards  the  light  or  away  from  it  —  or  the  light  is 
moved,  with  the  observer  stationary  — until  a  point  is  found 
at  which  the  large  letters,  as  the  capitals,  can  be  clearly  dis- 
tinguished, but  the  small  letters  are  indistinguishable.  This 
point  can  be  found  with  great  sharpness,  and  the  accuracy  of 


176  RADIATION,  LIGHT,  AND  ILLUMINATION. 

observation  by  the  luminometer  when  used  in  this  manner  is 
nearly  as  great  as  that  of  the  ordinary  photometer,  but,  unlike 
the  photometer,  the  luminometer  gives  consistent  and  reliable 
readings  even  with  widely  different  colors  of  light. 

The  comparisons  made  by  the  luminometer  of  widely  differ- 
ent colored  lights  by  different  observers  agree  remarkably 
well,  showing  that  the  distribution  of  color  sensitivity  is  prac- 
tically the  same  in  different  human  eyes.  Only  occasionally  a 
person  is  found  with  abnormally  low  sensitivity  for  some  par- 
ticular color  —  this  obviously  is  not  a  fault  of  the  instrument, 
but  in  the  nature  of  the  measured  object,  which  is  a  physiologi- 
cal effect,  and  as  such  may  be  different  in  different  persons. 

The  luminometer  can  be  still  further  improved  by  illuminat- 
ing one  half  of  the  printed  chart  from  the  one,  the  other  half 
from  the  other,  source  of  light,  and  then  moving  the  two  sources 
to  such  distances  that  the  small  letters  on  both  sides  of  the  chart 
become  indistinguishable,  while  the  capitals  are  distinguishable. 

As  well  known,  the  luminometer  is  largely  used  for  measuring 
street  illumination,  as  it  is  very  simple  and  requires  no  special 
technical  training.  Such  observations,  where  the  distances  are 
measured  by  pacing,  are  crude,  and,  to  get  exact  results  by  the 
luminometer,  the  same  care  is  required  as  when  using  the  pho- 
tometer. 

The  limitation  of  the  luminometer,  as  generally  used,  is  that 
it  compares  lights  at  constant  and  relatively  low  intensity  of 
illumination.  The  relative  intensity  of  light  sources  of  differ- 
ent colors  changes  however  over  a  wide  range  with  the  inten- 
sity of  illumination  at  which  they  are  compared,  as  discussed 
in  Lecture  III.  A  complete  comparison  of  different  colored 
lights  therefore  requires  measurements  at  different  intensities 
of  illumination. 

With  a  photometer,  the  intensity  of  illumination  can  usually 
be  varied  over  a  wide  range  by  bringing  the  light  sources 
nearer  to  the  screen  or  removing  them  farther.  In  the  lumi- 
nometer, only  a  moderate  change  of  the  intensity  of  illumina- 
tion, at  which  the  comparison  is  made,  can  be  produced  by 
using  different  sizes  of  print,  and  the  interpretation  of  such 
tests  is  difficult. 

A  wide  and  definite  range  of  intensities  of  illumination,  at 
which  comparison  of  the  light  sources  is  made  by  the  lumi- 


MEASUREMENT  OF  LIGHT  AND  RADIATION.        177 

nometer,  can  be  secured  by  using  gray  print  on  white  back- 
ground, and  lights  of  different  colors  thereby  compared  over 
a  wide  range  of  illuminations. 

With  a  luminometer  chart  of  gray  letters,  of  albedo  a,  on 
white  background,  the  illumination  or  light  flux  density,  at 
which  the  luminometer  readings  are  made  as  described  above, 
is: 


where  i0  is  the  illumination  or  light  flux  density  when  using 
black  print  on  white  background. 

81.  Since  light  is  a  physiological  effect,  the  measurement  of 
this  effect  requires  a  physiological  unit,  which  is  more  or  less  arbi- 
trarily chosen.  Such  a  unit  may  be  a  unit  of  light,  that  is,  of 
light  intensity  or  light  flux,  as  a  flame,  or  it  may  be  a  unit  of 
light-flux  density  or  illumination,  that  is,  of  light  flux  per  unit 
area. 

Thus,  a  fairly  rational  unit  of  light-flux  density  or  illumination 
would  be  the  illumination  required  at  the  limits  of  distinguish- 
ability  of  black  print  of  a  specified  type,  on  white  back- 
ground, that  is,  the  light  flux  per  unit  area  by  which,  with  such 
black  print  on  white  background,  the  capitals  and  large  letters 
can  still  be  distinguished,  while  the  small  letters  are  indistin- 
guishable. 

Usually  so-called  "  primary  standards "  have  been  chosen  as 
units  of  light  intensity.  Violle  recommended  as  standard  the 
light  at  right  angles  from  1  sq.  cm.  of  melting  platinum.  (Ap- 
proximately 20  cp.)  This  unit  has  never  been  introduced, 
partly  due  to  the  difficulty  of  producing  it,  partly  due  to  the 
unsuitability  of  platinum  for  this  purpose:  platinum  gives 
gray-body  radiation,  therefore  any  impurity,  as  a  trace  of  car- 
bonized dust,  may  increase  the  light. 

Candles  have  been  largely  used  for  standards,  as  the  name  of 
the  unit  implies,  made  and  burned  under  definite  specifications. 
As  individual  candles  vary  widely  in  their  light,  the  use  of  the 
candle  as  standard  necessarily  is  very  crude  and  inaccurate, 
and  thus  unsatisfactory. 

The  only  primary  standard  which  has  found  extensive  and 
international  use  is  the  amyl-acetate  lamp  of  Hefner.  This  is 
a  lamp  burning  arnyl  acetate  at  a  definite  rate,  with  a  definite 


178  RADIATION,  LIGHT,  AND  ILLUMINATION. 

height  of  flame  and  definite  conditions  regarding  air  pressure 
and  humidity.  This  Hefner  lamp,  or  German  candle,  equals 
about  90  per  cent  of  the  British  candle  and  equals  90  per  cent  of 
the  international  candle.  Amyl  acetate  has  been  chosen,  as  it 
can  easily  be  produced  in  chemical  purity,  and  gives  a  good 
luminous  flame.  The  flame,  however,  is  somewhat  reddish,  thus 
markedly  different  from  the  color  of  the  carbon  incandescent 
lamp,  and  departs  still  much  more  from  that  of  the  tungsten 
lamp.  Instead  of  amyl  acetate,  pentane  has  been  used  and  is 
still  used.  It  gives  a  somewhat  whiter  flame,  but  the  pentane 
lamp  is  not  as  constant. 

However,  the  Hefner  lamp,  while  universally  used  as  pri- 
mary standard,  is  altogether  too  inconvenient  for  general  pho- 
tometric use,  and,  for  this  purpose,  usually  incandescent  lamps 
are  employed  which  have  been  compared  with,  and  standard- 
ized by,  the  Hefner  lamp.  In  reality,  from  these  standard 
incandescent  lamps,  by  comparison,  other  incandescent  lamps 
have  been  standardized,  and  so  on,  until  of  late  years  the 
Hefner  lamp  has  been  finally  abandoned  as  primary  standard  of 
light,  and  we  have  no  primary  standard;  but  the  standard  of 
light  is  maintained  by  comparison  with  incandescent  lamps 
kept  for  this  purpose;  that  is,  it  is  maintained  by  duplication  of 
samples,  and  by  international  agreement  an  incandescent  lamp 
unit  has  been  adopted  as  the  standard  or  "  international  candle." 

82.  A  number  of  primary  standards  have  lately  been  pro- 
posed, but  none  has  yet  been  much  developed. 

Some  work  was  done  on  the  acetylene  flame,  burning  in 
oxygen.  It  has  a  very  suitable  white  color,  but  its  intensity  is 
very  sensitive  to  slight  impurities  of  the  acetylene,  and  such 
impurities,  as  hydrogen,  are  difficult  to  avoid. 

A  suitable  unit  appears  to  be  the  normal  temperature  radiation 
at  specified  temperature,  and  the  temperature  could  be  defined 
by  the  ratio  of  the  radiation  power  of  definite  wave  lengths. 
Thus,  such  a  unit  would  be  an  incandescent  lamp,  radiating  x 
watts  at  such  temperature  that  the  power  radiated  between  wave 
lengths  45  and  55  bears  to  the  power  radiated  between  wave 
lengths  60  to  70  the  ratio  y.  The  radiated  power  x  could  prob- 
ably be  determined  from  electric  power  input  and  losses.  Such 
a  unit  would  probably  be  replaceable  with  considerable  exact- 
ness, but  would  still  be  arbitrary. 


MEASUREMENT  OF  LIGHT  AND  RADIATION.        179 

A  further  possible  unit  would  be  the  light  given  by  one  watt 
visible  radiation,  by  normal  temperature  radiation  at  a  definite 
temperature  —  the  latter  specified  and  measured  by  the  ratio 
of  radiation  power  of  two  different  ranges  of  wave  length. 
Such  definition  would  base  the  physiological  effect,  under  speci- 
fied conditions  of  temperature,  on  the  unit  of  power,  or  the 
watt,  as  unit  of  light.  Its  disadvantage  is  the  difficulty  of 
measuring  the  power  of  the  total  visible  radiation,  since  at  the 
ends  of  the  visible  spectrum  the  power  is  high  and  the  physio- 
logical effect  low,  and  a  small  error  in  the  limits  of  the  spectrum 
would  make  a  considerable  error  in  the  result. 

More  satisfactory,  therefore,  appears  the  derivation  of  a 
primary  standard  of  light  by  combining  three  primary  colors  of 
light  in  definite  power  proportions.  Thus,  choosing  three  lines 
of  the  mercury  spectrum  —  in  the  mercury  arc  in  a  vacuum, 
perfect  steadiness  and  high  intensity  can  easily  be  produced  — 
in  the  red,  green  and  blue,  about  equidistant  from  each  other, 
these  three  radiations  would  be  combined  in  definite  propor- 
tions —  chosen  so  as  to  give  the  desired  color  of  the  light, 
probably  a  yellowish  white  —  and  in  such  qualities  as  to 
give  one  watt  total  radiation,  or,  if  as  unit  the  illumination 
is  used,  to  give  one  microwatt  per  sq.  cm.;  that  is,  the 
standard  of  illumination  would  be  the  illumination  produced 
by  one  microwatt  of  radiation  power,  composed  of  the  three 
wave  lengths  of  the  three  chosen  mercury  lines,  in  definite 
proportions. 

Such  a  standard,  derived  by  combination  of  definite  wave 
lengths,  which  are  easily  reproducible,  appears  the  most  satis- 
factory in  regard  to  permanence.  It  would  incidentally  give  a 
numerical  expression  to  color  values,  as  any  color  then  would 
be  represented  by  the  numerical  ratio  of  the  power  of  the  three 
standard  spectrum  radiations,  which,  mixed  together,  give  the 
color.* 

83.  Light  is  produced  for  the  purpose  of  illumination.  The 
raw  material  used  in  illumination  is  the  flux  of  light  issuing 
from  the  illuminant.  The  important  characteristic  of  the  illu- 
minant,  by  which  it  is  judged,  thus  is  the  total  flux  of  light 
issuing  from  it,  and  its  measurement  one  of  the  main  objects 
of  photometry. 

*  Proc.  A.  I.  E.  E.,  (1908). 


180 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


The  photometer  or  luminometer,  however,  gives  the  light 
intensity  in  one  direction  only.  Thus,  to  measure  the  total 
flux  of  light,  the  light  intensity  in  all  directions  in  space 
must  be  determined,  and  added,  or  averaged,  to  get  the 
average  intensity  of  light,  usually  called  the  "mean  spherical 
intensity." 

If  the  light  intensity  were  the  same  in  all  directions,  one 
single  photometric  observation  would  give  it,  and  therefrom,  by 
multiplying  with  4  TT,  the  total  flux  of  light  would  be  obtained. 
This,  probably,  is  never  the  case. 

Many  illuminants,  however,  give  a  symmetrical  distribution 
of  light  around  an  axis,  so  that  the  distribution  curve  is  the 
same  in  all  meridians.  This  is  practically  the  case  with  the  or- 
dinary incandescent  lamp  with  oval  filament,  and  also  with  the 
tantalum  and  the  tungsten  lamp.  Thus  if  the  curve,  shown  in 
Fig.  59,  is  the  distribution  curve  in  one  meridian,  it  is  the  same 


FIG.  59. 

in  every  other  meridian,  and  for  photometric  test  of  the  illumi- 
nant  it  is  sufficient  to  measure  the  light  intensities  in  one  merid- 
ian only,  for  instance,  from  10  to  10  degrees.  To  get  herefrom 
the  mean  or  average  intensity,  it  would  obviously  be  wrong  to 
merely  average  all  the  intensities  under  equal  angles,  since  the 
equatorial  intensity  covers  a  far  greater  area  —  a  zone  of  10  de- 
grees width  and  2  x  circumference  —  than  the  intensity  of  lati- 
tude <j>j  that  is,  under  angle  <f>  from  the  horizontal:  the  latter 
covers  a  zone  of  10  degrees  width  and  2  it  cos  $  circumference, 
and  the  polar  intensity  covers  only  a  point. 
To  get  the  total  flux  of  light,  the  intensity  under  each  angle  <£ 


MEASUREMENT  OF  LIGHT  AND  RADIATION.        181 

thus  is  to  be  multiplied  with  the  area  of  the  zone  which  it 
covers,  2  nd  cos  <j>,  where  d  is  the  angular  width  of  the  zone 
(10  deg.,  for  instance),  and  then  added.  The  average  or  mean 
spherical  intensity  then  is  derived  herefrom  by  dividing  with 
the  surface  of  the  sphere,  or  by  4  re. 

Thus,  to  get  the  mean  spherical  intensity  from  the  distribu- 
tion curve,  the  instantaneous  values  of  intensity,  taken  under 

equal  angles  d,  are  multiplied  each  by  cos  <£,  then  added,  and 
ft 

the  sum  multiplied  by  -,  where  d,  the  angular  distance  under 

2 

which  observations  are  taken,   is  given  in  radians,   that  is, 

10  deg.  gives  d  =  — -  TT.    This  usually  is  done  graphically. 
180 

Occasionally,  as  in  incandescent  lamps  with  single-loop  fila- 
ment, the  light  intensity  is  not  the  same  in  all  meridians,  but  a 
maximum  in  two  opposite  meridians:  at  right  angles  to  the 
lamp,  and  a  minimum  in  the  two  meridians  at  right  angles  to 
the  former,  giving  a  horizontal  or  equatorial  distribution  of 


FIG.  60. 

light  intensity  about  as  shown  in  Fig.  60.  In  this  case  the 
horizontal  distribution  curve  may  also  be  determined  photo- 
metrically, averaged  so  as  to  give  the  mean  horizontal  intensity 


182  RADIATION,  LIGHT,  AND  ILLUMINATION. 

and  the  ratio  of  the  mean  horizontal  intensity  to  the  maximum 
horizontal  intensity  (or  any  other  definite  horizontal  inten- 
sity); and  the  mean  spherical  intensity,  as  derived  from  the 
meridian  of  maximum  horizontal  intensity  (or  any  other  definite 
horizontal  intensity),  is  multiplied  with  this  ratio  to  get  the 
real  mean  spherical  intensity.  Usually  in  this  case  measure- 
ments are  taken  only  in  one  meridian,  but  during  the  test  the 
lamp  rotated  around  its  vertical  axis  with  sufficient  speed,  so 
that  each  observation  in  the  meridian,  under  angle  <£,  in  reality 
is  the  mean  intensity  in  the  direction  <f>.  Thus,  in  incandes- 
cent lamp  tests,  usually  the  lamp  is  revolved,  so  as  to  average 
between  the  different  meridians. 

As  the  distribution  of  intensity  in  the  meridian  is  the  same, 
within  the  error  of  photometric  test,  for  all  incandescent  lamps 
of  the  same  type  of  filament,  usually  the  distribution  curve  of 
one  meridian  is  measured  once  for  all,  therefrom  the  ratio  of 
horizontal  to  mean  spherical  candle  power,  the  so-called  spherical 
reduction  factor,  determined,  and  then  in  further  photometric 
tests  of  lamps  of  this  type  only  the  horizontal  intensity  meas- 
ured, and  from  this,  dividing  by  the  spherical  reduction  factor, 
the  mean  spherical  intensity  is  derived.  Thus,  while  with  the 
incandescent  lamp  the  intensity  varies  in  each  meridian,  and  is 
different  in  the  different  meridians,  the  mean  spherical  intensity 
nevertheless  is  derived  by  a  single  photometric  observation  of 
the  horizontal  intensity  with  rotating  lamp:  the  rotation  aver- 
ages between  the  different  meridians,  and  the  spherical  reduction 
factor  translates  from  horizontal  to  mean  spherical  intensity. 
Reduction  factors  of  incandescent  lamps  usually  are  between 
0.75  and  0.80. 

84.  Far  more  difficult  is  the  matter  with  arc  lamps :  in  the  ordi- 
nary carbon  arc  lamp,  the  intensity  also  varies  in  the  meridian, 
and  is  different  in  the  different  meridians,  but  not  with  the 
same  regularity  as  in  the  incandescent  lamp,  and,  further- 
more, the  intensity  distribution  between  the  different  meridi- 
ans, as  well  as,  to  a  lesser  extent,  the  total  light  flux  of  the 
lamp,  varies  with  the  time.  The  arc  is  not  steady  and  con- 
stant in  position,  as  the  incandescent  filament,  but  wanders, 
and  the  light  intensities  on  the  side  of  the  lamp,  where  the  arc 
happens  to  be,  thus  are  greater  than  on  the  side  away  from  the 
arc.  The  meridians  of  maximum  and  of  minimum  intensity, 


MEASUREMENT  OF  LIGHT  AND  RADIATION.        183 

however,  do  not  remain  constant  in  position,  but  continuously 
change  with  the  wandering  of  the  arc.  Therefore,  by  measure- 
ments in  a  single  meridian,  the  distribution  curve  of  maximum 
and  that  of  minimum  intensity  can  be  determined  by  waiting 
during  the  observation  for  the  arc  to  come  around  to  the 
side  of  the  observer  —  maximum  —  and  go  to  the  opposite 
side  — minimum — intensity.  Such  curves  are  shown  in  Fig.  61. 


FIG.  61. 

This,  however,  carried  out  for  every  angle  in  the  meridian, 
makes  arc-light  photometry  rather  laborious,  especially  as 
the  total  intensity  pulsates  with  the  time,  and  therefore  a 
considerable  number  of  readings  have  to  be  taken  in  every 
position. 

Therefore,  for  arc  light  photometry,  integrating  photometers 
are  especially  desirable,  that  is,  photometers  which,  by  a  single 
observation,  determine — more  or  less  accurately — the  mean 
spherical  intensity;  that  is,  the  average  intensity, in  all  directions. 
With  such  an  integrating  photometer,  by  taking  a  number  of 
successive  readings  and  averaging,  so  as  to  eliminate  the  varia- 
tion of  total  intensity  with  the  time,  the  mean  spherical  inten- 
sity, and  thus  the  total  flux  of  light,  can  be  derived  more 
rapidly. 

Such  an  integrating  photometer  is  the  Matthews  photometer. 
It  consists  of  a  circle  of  inclined  mirrors,  which  surround  the 
lamp  and  reflect  the  light  in  all — or,  rather,  a  certain  number 
of  —  different  angles  into  the  photometer,  and  there  the  differ- 
ent reflected  beams  are  by  absorption  reduced  in  the  proportion 


184          RADIATION,  LIGHT,  AND  ILLUMINATION. 

of  cos  (f>  and  combined  on  the  photometer  screen.  Obviously, 
the  Matthews  photometer  does  not  average  the  intensity  in  all 
directions,  but  only  in  two  meridians  opposite  to  each  other; 
however,  by  averaging  a  number  of  successive  readings,  very 
accurate  results  can  be  derived. 

A  method  of  averaging  in  all  directions  is  based  on  a  similar 
principle  as  that  by  which  the  radiation  from  the  interior  of  a 
closed  sphere  of  constant  temperature  was  found  to  be  black- 
body  radiation:  if  the  lamp  is  located  in  the  center  of  a  closed 
sphere  (perforated  only  at  the  place  where  the  photometer 
enters)  of  perfectly  white  reflecting  surface,  then  the  light  in- 
tensity throughout  the  entire  inner  surface  of  the  sphere  is 
uniform,  and  is  the  mean  spherical  intensity  of  illumination  at 
the  distance  of  the  radius  of  the  sphere.  The  reason  is :  every 
element  of  the  interior  of  the  sphere  receives  light  directly  from 
the  lamp,  and  also  light  reflected  from  all  the  other  elements 
of  the  sphere,  so  that  the  total  light  received  at  every  element 
of  the  sphere  is  the  same,  hence  is  the  average  illumination. 
By  enclosing  the  test  lamp  in  the  center  of  such  a  photometric 
sphere  of  sufficient  size,  its  mean  spherical  intensity  thus  can  be 
determined  by  a  single  reading.  Such  an  arrangement  has  the 
further  advantage  that  it  allows  a  direct  measurement  of  mean 
spherical  intensity  —  or  light  flux  —  of  such  illuminants  as  the 
mercury  lamp,  in  which  the  radiator  is  of  such  extent  that  it 
cannot  be  considered  as  a  point  without  going  to  excessive 
distances. 

85.  Photometrically,  and  in  illuminating  engineering,  only 
the  mean  spherical  intensity  —  which  represents  the  total  flux 
of  light  —  and  the  distribution  curve — which  represents  the 
distribution  of  this  light  in  space  — are  of  importance.  The 
"horizontal  intensity7'  has  been  used  as  a  conventional  rating 
of  incandescent  lamps,  but  is  merely  fictitious,  as  it  does  not 
mean  an  actual  average  horizontal  intensity,  but  the  horizontal 
intensity  which  the  light  flux  of  the  lamp  would  give  with  the 
standard  mean  spherical  reduction  factor,  if  the  filament  had 
the  standard  shape. 

Downward  candle  power  and  maximum  candle  power  obvi- 
ously have  no  meaning  regarding  the  light  flux  of  the  lamp, 
but  merely  represent  a  particular  feature  of  the  distribution 
curve. 


MEASUREMENT  OF  LIGHT  AND  RADIATION.        185 

Hemispherical  candle  power  is  used  to  some  extent,  especially 
abroad.  It  is  a  mixture  between  light  flux  and  distribution 
curve,  and  as  it  gives  no  information  on  the  total  light  flux,  nor 
on  the  actual  distribution  curve,  and  may  mislead  to  attribute 
to  the  lamp  a  greater  light  flux  than  it  possesses  —  by  mistaking 
it  with  mean  spherical  candle  power  —  it  has  no  excuse  for  exist- 
ence, and  should  not  be  used. 


LECTURE  X. 
LIGHT   FLUX   AND    DISTRIBUTION. 

86.  The  light  flux  of  an  illuminant  is  its  total  radiation 
power,  in  physiological  measure.  It  therefore  is  the  useful 
output  of  the  illuminant,  and  the  efficiency  of  an  illuminant 
thus  is  the  ratio  of  the  total  light  flux  divided  by  the  power 
input. 

In  general,  the  distribution  of  the  light  flux  throughout  space 
is  not  uniform,  but  the  light-flux  density  is  different  in  different 
directions  from  an  illuminant. 

Unit  light-flux  density  is  the  light-flux  density  which  gives 
the  physiological  effect  of  one  candle  at  unit  distance.  The 
unit  of  light  flux,  or  the  lumen,  is  the  light  flux  passing  through 
unit  surface  at  unit  light-flux  density.  The  unit  of  light  inten- 
sity, or  one  candle,  thus  gives,  if  the  light-flux  distribution  is 
uniform  in  all  directions,  unit  flux  density  at  unit  distance  from 
the  radiator,  and  thus  gives  a  total  flux  of  light  of  4  it  units,  or 
4  it  lumens  (since  the  area  at  unit  distance  from  a  point  is  the 
surface  of  a  sphere,  or  4  it). 

The  unit  of  light  intensity,  or  the  candle  power  thus  given, 
with  a  radiator  of  uniform  light-flux  distribution,  4  x  lumens  of 
light  flux,  and  inversely,  a  radiator  which  gives  4  it  lumens 
of  light  flux,  gives  an  intensity  of  one  candle,  if  the  intensity  is 
uniform  in  all  directions,  and,  if  the  distribution  of  the  intensity 
is  not  uniform,  the  average  or  mean  spherical  intensity  of  the 
radiator  is  one  candle.  Thus  one  mean  spherical  candle  rep- 
resents 4  it  lumens  of  light  flux,  and  very  frequently  the  mean 
spherical  candle  is  used  as  representing  the  light  flux:  the  light 
flux  is  4  TT  times  the  mean  spherical  intensity,  and  the  mean 
spherical  intensity  is  the  total  light  flux  divided  by  4  it,  regard- 
less whether  the  light  flux  is  uniformly  distributed  or  not. 

The  total  light  flux  of  an  illuminant  is  derived  by  the  sum- 
mation or  integration  of  the  intensities,  that  is,  the  flux  den- 
sities at  unit  distance,  in  all  directions  from  the  radiator. 

186 


LIGHT  FLUX  AND  DISTRIBUTION.  187 

The  distribution  of  light  flux  or  of  intensity  is  never  uniform, 
and  the  investigation  of  intensity  distribution  of  the  light  flux 
thus  necessary. 

The  distribution  of  the  light  intensity  of  an  illuminant  de- 
pends upon  the  shape  of  the  radiator  and  upon  the  objects 
surrounding  it;  that  is,  the  distribution  of  the  light  flux  issuing 
from  the  radiator  depends  on  the  shape  of  the  radiator,  but 
is  more  or  less  modified  by  shadows  cast  by  surrounding 
objects,  by  refraction,  diffraction,  diffusion  in  surrounding 
objects,  etc. 

The  most  common  forms  of  radiators  are  the  circular  plane, 
the  straight  line,  that  is,  the  cylinder,  the  circular  line  or  circular 
cylinder  and  combinations  thereof. 

87.  Very  frequently  the  intensity  distribution  of  an  illumi- 
nant is  symmetrical,  or  approximately  symmetrical,  around  an 
axis.  This,  for  instance,  is  the  case  with  the  arc  lamp,  the 
incandescent  lamp,  most  flames,  etc.  If  the  distribution  is 
perfectly  symmetrical  around  an  axis,  the  distribution  in  space 
is  characterized  by  that  in  one  meridian,  that  is,  one  plane  pass- 
ing through  the  axis.  If  the  distribution  is  not  symmetrical 
around  the  axis,  usually  the  space  distribution  is  characterized 
by  the  distribution  curves  in  two  meridians  at  right  angles  to 
each  other,  the  meridian  of  maximum  and  that  of  minimum 
intensity,  and  the  distribution  in  the  equatorial  plane,  that  is, 
the  plane  at  right  angles  to  the  axis. 

Distribution  curves  are  best  represented  in  polar  coordinates, 
and  the  angle  <f>  counted  from  the  axis  towards  the  equator 
(that  is,  complementary  to  the  "  latitude"  in  geography). 

As  most  illuminants  are  used  with  their  symmetry  axis  in 
vertical  direction,  and  the  downward  light  is  usually  of  greater 
importance,  it  is  convenient  in  plotting  distribution  curves  to 
choose  the  symmetry  axis  as  vertical,  and  count  the  angle  $ 
from  the  downward  vertical  towards  the  horizontal;  that  is, 
the  downward  beam  would  be  given  by  (f>  =  0,  the  horizontal 
beam  by  ^  =  90  deg.,  and  the  upward  beam  by  <j>  =  180  deg. 

The  usual  representation  of  the  light-flux  distribution  in  po- 
lar coordinates  does  not  give  a  fair  representation  of  the  total 
light  flux,  or  the  mean  spherical  intensity  of  the  light  source, 
but  on  the  contrary  frequently  is  very  misleading.  When  com- 
paring different  polar  curves  of  intensity  distribution,  it  is 


188  RADIATION,  LIGHT,  AND  ILLUMINATION. 

impossible  to  avoid  the  impression  of  the  area  of  the  curve  as 
representative  of  the  light  flux.  The  area  of  the  polar  curve, 
however,  has  no  direct  relation  whatever  to  the  total  light  flux, 
that  is,  to  the  output  of  the  illuminant,  since  the  area  depends 
upon  the  square  of  the  radii,  and  the  light  flux  directly  upon 
the  radii  of  the  curve.  Thus  an  illuminant  of  twice  the  inten- 
sity, but  the  same  flux  distribution,  gives  a  polar  curve  of  four 
times  the  area,  and  the  latter  gives  the  impression  of  a  source 
of  light  far  more  than  twice  as  great  as  the  former. 

The  meridian  curves  of  intensity  distribution  are  still  more 
misleading:  the  different  angles  of  the  curve  correspond  to 
very  different  amounts  of  light  flux:  the  horizontal  intensity 
(<£  =  90  deg.)  covers  a  zone  of  2  rn  circumference,  while  the 
intensity  in  any  other  direction  (f>  covers  a  zone  of  2  rn  sin  <j> 
circumference;  that  is,  an  area  which  is  the  smaller,  the  nearer 
(f>  is  to  0  or  180  deg. ;  the  terminal  intensity,  upward  or  down- 
ward, finally  covers  a  point  only,  that  is,  gives  no  light  flux. 
As  the  result  hereof,  an  illuminant  giving  maximum  intensity 
in  the  downward  direction,  and  low  intensity  in  the  horizontal, 
gives  a  much  larger  area  of  the  polar  curve  than  an  illuminant 
of  the  same  or  even  a  greater  total  light  flux  which  has  its 
maximum  intensity  in  the  horizontal.  Comparing,  therefore, 
illuminants  of  different  distribution  curves,  it  is  practically 
impossible  not  to  be  misled  by  the  area  of  the  polar  curve,  and 
thus  to  overestimate  the  illuminant  having  maximum  downward 
intensity,  and  underestimate  the  illuminant  having  maximum 
horizontal  intensity. 

The  misleading  nature  of  the  polar  curves  of  intensity  dis- 
tribution in  the  meridian  is  illustrated  by  the  curves  in  Figs. 
64  and  99:  the  three  curves  of  Fig.  64  give  the  same  total 
light  flux;  that  is,  the  same  useful  output;  but  2  looks  vastly 
greater  than  1  or  3,  and  3  especially  looks  very  small.  Curves 
0,  1,  2,  3,  4  in  Fig.  99  give  the  same  total  light  flux,  and  curve 
5  gives  only  one  tenth  the  light  flux.  To  the  eye,  however,  the 
curve  4  gives  the  impression  of  a  far  more  powerful  illuminant 
than  the  curve  1,  and  curve  5  appears  practically  equal,  if  not 
larger  than  1,  while  in  reality  it  represents  only  one  tenth  the 
light  output  of  1. 

88.  In  an  illuminant  in  which  the  distribution  of  intensity 
is  symmetrical  around  an  axis,  and  thus  can  be  represented 


LIGHT  FLUX  AND  DISTRIBUTION 


189 


by  one  meridian  curve,  the  total  light  flux  is  calculated  thus: 
Let  /  =  intensity  at  angle  <f> 

(counting  the  angle  <j>  from  one  pole  over  the  equator  to  the 
other  pole). 

This  intensity  covers  a  zone  of  the 
sphere  of  unit  radius  of  width  d(j>  and 
angle  <£,that  is,  a  zone  of  radius  (Fig.  62) 
r  =  sin<£;  thus  surface 

dA  =  2  n  sin 


and  the  light  flux  in  this  zone  therefore 
is: 


FIG.  62. 


=  27r/sin<M^ 
hence,  the  total  light  flux : 

<£  =  2  TT  /     /sin (f>d(/>. 
Jo 


CD 


(2) 


The  light  flux  in  the  space  from  the  downward  direction  </>  =  0 
to  the  angle  <£  =  fa  against  the  vertical  or  symmetry  axis,  then 
is 


fc1  =  2  TT        /  sin  <t>dfa  (3) 

*/0 

and  the  light  flux  in  a  zone  between  the  angles  (j)1  and  fa  is 

(4) 


I.    DISTRIBUTION  CURVES  OF  RADIATION. 

(1)   Point,  or  Sphere,  of  Uniform  Brilliancy. 

In  this  case,  the  intensity  distribution  is  uniform,  and  thus,  if 

/  =  intensity  of  light,  in  candles, 
<£=  4  nl  =  light  flux,  in  lumens;  (5) 

or,  inversely: 

<I> 
/  =  -.  (6) 

The  brilliancy  of  a  radiator  is  the  light-flux  density  at  its  sur- 
face.   Thus,  with  a  luminous  point  of  intensity  /,  the  brilliancy 


190 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


would  be  infinite;   with  a  luminous  sphere  of  uniform  intensity 
distribution,  and  of  radius  r,  the  brilliancy  is 

*          7  '  (7) 


B  = 


,2  ' 


hence,  inversely  proportional  to  the  square  of  the  radius  of  the 
spherical  radiator. 

(2)   Circular  Plane  of  Uniform  Brilliancy. 
89.   Such  radiators  are,  approximately,  the  incandescent  tip 
of  the  carbons  in  the    (non-luminous)  electric  carbon  arc,  or 
the  luminous  spot  in  the  lime  cylinder 
of  the  lime  light  (hydro-oxygen  flame), 
etc. 

Choosing  the  circular  luminous  plane 
as  horizontal  direction,  the  intensity 
distribution  is  symmetrical  around  the 
vertical,  the  vertical  direction  thus  can 
be  chosen  as  axis,  and  the  angle  <£ 
counted  from  the  vertical  upward. ' 

The  intensity  is  a  maximum  70,  ver- 
FlG-  63-  tically  downward,  for  <£  ==  0. 

In  any  other  direction,  under  angle  (f>  against  the  vertical 
(Fig.  63),  the  intensity  is 

/  =  /0  cos  <£,  (8) 

and  is  zero  for 

<£  =  90  deg. 

The  light  flux  issuing  from  the  radiator  below  angle  <f>  is,  by 
(3): 


hence,  by  (8) : 


rsin  (j)  cos  (f)d<f> 


-I.  /cos  2* 

&         I  I 


-/„{!  -cos  24,}, 


(9) 


LIGHT  FLUX  AND  DISTRIBUTION.  191 

and  the  total  light  flux,  from  (f>  =  0  to  <j>  =  90  deg.  =  —  ,  thus  is  : 

ft 


or 


The  brilliancy  of  the  source  of  light  is  the  total  light  flux 
divided  by  the  luminous  area;  or, 

* 


and,  if  r  =  radius  of  the  luminous  circle, 

A  =  ;rr2, 
and 


-?''  02) 

or, 

70  =  r2£;  (13) 

that  is,  the  same  as  in  class  (1). 

Comparing  (11)  with  (5),  it  thus  follows  that  the  total  light  flux 
of  such  a  radiator,  for  the  same  maximum  intensity,  is  only  one 
quarter  that  of  a  radiator  giving  uniform  intensity  distribution 
throughout  space,  or  inversely,  with  such  a  downward  distribution 
of  light,  the  maximum  intensity  is  four  times  as  great  as  it  would 
be  with  the  same  total  light  flux  uniformly  distributed  through 
space. 

The  flux  distribution  is  a  circle  having  its  diameter  from  the 
source  of  light  downward.  It  is  shown  as  2  in  Fig.  64,  and 
the  concentric  circle  giving  uniform  intensity  distribution  of 
the  same  total  light  flux  is  shown  as  1. 

(3)   Hollow  Circular  Surface. 

Such  a  radiator,  for  instance,  is  approximately  the  crater  of  the 
positive  carbon  of  the  arc  lamp. 

As  with  such  a  radiator,  as  shown  in  section  in  Fig.  65,  the 
projection  of  the  luminous  area  in  any  direction  <f>  is  the  same 


192  RADIATION,  LIGHT,  AND  ILLUMINATION. 


FIG.  64. 


FIG.  65. 


FIG.  66. 


LIGHT  FLUX  AND  DISTRIBUTION.  193 

as  with  the  plane  circular  radiator  (2),  the  same  equations 
apply. 

(4)   Rounded  Circular  Surface. 

Such,  for  instance,  is  approximately  the  incandescent  carbon 
tip  of  the  arc-lamp  electrodes,  when  using  carbons  of  sufficiently 
small  size,  so  that  the  entire  tip  becomes  heated. 

Assuming,  in  Fig.  66,  the  radiator  as  a  segment  of  a  sphere,  and 
let  2  aj  =  the  angle  subtending  this  segment,  rl  the  radius  of  this 
sphere. 

For  all  directions  <£,  up  to  the  angle  co  below  the  horizontal  : 

0<  0  <£-w  ; 

the  projection  of  the  spherical  segment  in  Fig.  66  is  the  same  as 
that  of  a  plane  circle,  and  thus  the  intensity  is  given  in  class  (1), 
as: 

i  =  70  cos  (/>. 

In    the    direction,  --  -  co  <<£<-,  however,   the    intensity  is 

A  2i 

greater,  by  the  amount  of  light  radiated  by  the  projection  Dyx, 
and,  in  the  horizontal  direction,  the  intensity  does  not  vanish, 
but  corresponds  to  the  horizontal  projection  of  the  luminous 
segment. 
Above  the  horizontal,  light  still  issues  in  the  direction, 


from  the  segment  Buv,  and  only  for  -  +  co  <  <j>  does  the  light 

Zi 

cease. 

If  r2  =  radius  of  carbon,  the  radius  of  the  luminous  segment  is 


sin  co' 


the  height  of  the  segment  is 

h  =  rl  (1  —  cos  co) 
r2  (1  —  cos  co) 


sin  co 


194          RADIATION,  LIGHT,  AND  ILLUMINATION, 
hence  the  surface  of  the  segment,  or  the  luminous  area,  is 
A2  =  2  rjin 

2  r227r  (1  —  cos  w) 


2r227r  X  2  sin2 


•       2  2 

4  sin2  -  cos    - 
Z  2 


COS   2 


(14) 


Thus,  if  the  luminous  area  is  the  same  as  in  the  plane  circle 
class  (2),  it  must  be: 

TV2  7T 


r2  =  rcos~;  (15) 

and,  if  the  brilliancy  B  is  the  same,  the  maximum  intensity  for 
<t>  =  Ois 


cos2     ;  (16) 

that  is,  the  rounding  off  of  the  circular  radiator,  at  constant  bril- 
liancy and  constant  luminous  surface,  decreases  the  maximum 

intensity  70  by  the  factor  cos2-,  but  increases  the  intensity  within 

the   angle   from   co  below   to   a>   above   the  horizontal   direc- 
tion. 

In  Fig.  67  are  plotted  the  distribution  curves,  for  the  same 
brilliancy  and  the  same  area  of  the  radiator,  for  a  plane  circular 
radiator,  as  1  ;  a  rounded  circular  radiator  of  angle  co  =  30  deg. 
as  2,  and  a  rounded  circular  radiator  of  angle  a>  =  60  deg., 


LIGHT  FLUX  AND  DISTRIBUTION. 


195 


as  3.  As  seen,  with  increasing  rounding,  gradually  more  and 
more  light  flux  is  shifted  from  the  vertical  into  the  horizontal 
direction. 


FIG.  67. 


Straight  Line  or  Cylindrical  Radiator. 

90.  Such  radiators  are  represented  approximately  by  the  lum- 
inous arcs  with  vertical  electrodes,  by  the  mercury-arc  tube, 
by  straight  sections  of 
incandescent-lamp  fila- 
ments, etc. 

The  intensity  distribu- 
tion is  symmetrical  with 
the  radiator  as  axis. 

The  intensity  is  a  max- 
imum 70  at  right  angles 
1,1  T  i  •  FIG.  68. 

to   the    radiator,    or   in 

horizontal  direction,  <j>  =  90  deg.,  when  choosing  the  radiator  as 
vertical  axis.    At  angle  <£,  the  intensity  is,  Fig.  68, 

I  =  /o  sin  0,  (17) 

and  is  zero  for  </>  =  0  and  (f>  =  180  deg.,  or  in  the  vertical. 


196  RADIATION,  LIGHT,  AND  ILLUMINATION. 

The  light  flux  within  angle  <f>  from  the  vertical  is,  by  (4), 


=  7r/0    f   (l-co 

«^o 

hence,  ,  A        _    /  .      sin  2 


and  the  total  light  flux  for  (f>  =  K  is 

*  =  »v.;  (19) 

or,  inversely:  ^_  ^    ?  :  (2Q) 

and  the  radiating  surface  is 

A  =  ^  (21) 

where  Z  is  the  length;  w  the  diameter  of  radiator.      The  bril- 
liancy, therefore,  is  ^ 


(22) 


may  be  called  the  linear  maximum  intensity,  or,  maximum  inten- 
sity per  unit  length. 

Most  of  the  light  'of  a  linear  vertical  radiator  issues  near  the 
horizontal,  very  little  in  downward  and  upward  direction.  Put- 
ting <J>0  =  J  $,  gives  the  angle  <f>,  which  bisects  the  light  flux  : 

sin  2  (f>      n 
*      —    =4' 

and  herefrom,  by  approximation,  $  =  66  deg.;  that  is,  half  the 
light  flux  issues  within  the  narrow  zone  from  24  deg.  below  to 


LIGHT  FLUX  AND  DISTRIBUTION. 


197 


24  deg.  above  the  horizontal,  or  in  the  space  between  a  and  a'  in 
Fig.  68. 

It  is  interesting  to  compare  the  three  radiators,  (1),  (2),  and  (5), 
on  the  basis  of  equal  maximum  intensity,  and  on  the  basis  of 
equal  light  flux,  thus : 


Light  flux  <£,  at  equal  maximun 
intensity  /0 

Maximum  intensity  70,  at  equal 
light  flux  $ 


Uniform. 
47T/0 

4 

4^ 
1 


Circle.  Cylinder. 


7T=   3.14 


1=1.27 

7T 


As  seen,  at  the  same  maximum  intensity,  the  cylinder  gives 
nearly  as  much  light  flux  as  given  by  uniform  distribution,  that 
is,  its  deficiency  in  intensity  in  the  polar  regions  represents  very 
little  light  flux.  The  circular  plane,  however,  gives  only  one 
quarter  as  much  light  flux  as  uniform  distribution. 

With  the  same  horizontal  intensity  of  a  cylindrical  radiator, 
as  the  vertical  intensity  of  a  circular  plane,  the  former  gives 
TT  =  3J4  times  the  flux  of  light. 

In  Fig.  64  the  three  distribution  curves  are  shown  for  the  same 
total  flux  of  light:  curve  1  for  uniform  intensity,  2  for  a  plane 
circle,  and  3  for  a  straight  cylinder  as  radiator. 

(6)   Circular  Line  or  Cylinder. 

In  the  spirals,  loops  or  ovals  of  in- 
candescent-lamp filaments,  circular 
radiators,  or  sections  thereof,  are  met. 

Let  r  =  radius  of  the  circular  radi- 
ator, w  =  diameter  of  the  radiator 
cylinder,  shown  in  section  in  Fig.  69. 

The  intensity  is  a  maximum  in  the 
direction  at  right  angle  to  the  plane 
of  the  circle. 

The  projection  of  the  radiator  in  this  direction  of  maximum 
intensity,  $  =  0,  has  the  length:  2  TIT;  and  if,  by  (24)  : 

wB 


69- 


maximum  linear  intensity, 


198  RADIATION,  LIGHT,  AND  ILLUMINATION. 

where  B  =  brilliancy, 

it  is,  IQ=27rrIQ'=2rwB.  (25) 

This  is  in  the  direction  in  which  the  projection  of  the  radiator 
is  a  circle  of  radius  r,  and  thus  circumference  2  TTT. 

In  any  other  direction  </>,  the  projection  of  the  radiator  is  an 
ellipse,  with  r  and  r  cos  (f>  as  half  axes,  as  seen  from  Fig.  69. 

If  I  =  the  circumference  of  this  ellipse,  the  intensity  in  the 
direction  <j>  bears  to  the  maximum  intensity  70  the  same  ratio  as 
the  circumference  of  the  ellipse  to  that  of  the  circle;  that  is, 

I-It^—Ifl.  (26) 

2  nr 

The  circumference  of  an  ellipse  with  the  half  axes  a  and  c  is 

I  =  (a  +  c)  n  (1  +  q), 

I/a  -  c\2      1  /a  -  c\4       1    /a  -  c\8  W 

4  \a  +  c)  +  64  Va  +  c)  +  256\a  +  c)  +  '  ' 


where 


The  ratio  of  the  circumference  of  the  ellipse  to  its  maximum 
diameter,  y  =  — ,  is  given  in  Table  I,  and  plotted  in  Fig.  70, 

w  T 

with  the  ratio  of  the  half  axes,  that  is,  cos  <p,  as  abscissas,  and,  in 
Fig.  71,  with  angle  <f>  as  abscissas. 

TABLE  I.  — CIRCUMFERENCE  OF  ELLIPSE. 


c 

-  —  COS  d>. 

a 

V  =  Tr- 

f 

V=ir- 

1.0 

1.571-  s 

0 

1.571  =  5 

2 

2 

0.9 

.495 

10 

1.560 

0.8 

.418 

20 

1.525 

0.7 

.345 

30 

1.470 

0.6 

.278 

40 

1.390 

0.5 

.210 

45 

1.350 

0.4 

.150 

50 

1.305 

0.3 

.110 

60 

1.220 

0.2 

.055 

70 

1.120 

0.1 

.025 

80 

1.045 

0 

.000 

90 

1.000 

LIGHT  FLUX  AND  DISTRIBUTION. 


199 


\ 

y  - 

1.5 
1.4 
1.3 
1.2 
1.1 
1.0 
0.9 
0.8 
0.7 
0.6 
0.5 
0.4 
0.3 
0.2 
0.1 

\ 

X 

N 

X 

X. 

X 

^ 

\ 

^ 

C( 

£ 

minimum  p, 
mayimu/Ti 

imet 

erof 

Ellii 

sis 

0 

I     0 

,i. 

4    0*5    0 

6     0 

7     0 

8     0 

9 

-^v 

1.5 
1.4 
1.3 
1.2 

1.1 
1.0 
0.0 
0.8 
0.7 
0.6 
0.5 
0.4 
0.3 
0.2 
'0.1 

^ 

\ 

\ 

\ 

^ 

x 

^ 

V, 

1 

2 

Angle^Deglrees 
0     3.0     40     1?0     6 

0      *i 

tt      f 

> 

FIG.  70. 


FIG.  71. 


In  Fig.  72  is  plotted  the  intensity  distribution  in  the  meridian 


of  such  a  circular  radiator. 


This  shows  a  maximum  70  in  the 


vertical,  and  a  minimum ^=  —  70 

7T 

in  the  horizontal. 

Theoretically,    exactly  in    the 
horizontal,   <f>  =  90  deg.,  the  in- 
tensity should  be  ~,  as  one  half 
ft 

of  the  circle  shades  the  other 
half.  In  most  cases  of  such  circular 
radiators,  sections  of  incandescent- 
lamp  filaments,  w  is  so  small  com- 
pared with  r,  that  it  is  practically 
impossible  to  have  the  radiator 
perfectly  in  one  plane,  as  would  be 
required  for  one  half  to  shade  the 
other  half. 

(7)   Single-Loop  Filament. 


FIG.  72. 


200 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


92.  As  an  illustration  of  the  use  of  the  distribution  curves 
of  different  typical  forms  of  radiators,  the  distribution  curves 
of  a  single-loop  incandescent-lamp  filament  may  be  calcu- 
lated. 

Such  a  filament  consists  of  two  straight  sides,  joined  by  a  half 
circle,  as  shown  in  Fig.  73. 

The  distribution  of  in- 
tensity is  not  symmetrical 
around  any  axis,  but  ap- 
proximately so  around  the 
axis  Z  in  Fig.  73. 

The  meridian  of  maxi- 
mum intensity  is  the  plane 
YZ,  at  right  angles  to  the 
plane  of  the  filament  ;  the 
meridian  of  minimum  in- 
tensity is  the  plane  of  the 
filament,  XZ,  and  the 
least  variation  of  intensity 
occurs  in  the  equatorial 
plane  XY.  The  distribu- 
tion curves  in  all  three  of 
.these  planes  are  required. 
Assuming  the  straight 
sides  as  of  a  length  equal 
to  twice  the  diameter  of 
the  loop,  or  of  length  4  r, 
where  r  =  radius  of  the  half  circle. 

As  it  is  impossible  to  produce  and  maintain  such  a  filament 
perfectly  in  one  plane,  we  assume,  as  average  deviation  of  the  two 
straight  sides  A  and  B  of  Fig.  73  from  the  vertical,  an  angle  of 
10  deg. 

The  intensity  distribution  of  the  straight  sides  A  and  B  in  any 
meridian  plane  thus  is  that  of  a  straight  radiator,  (5),  at  an 
angle  of  10  deg.  against  the  vertical. 

Let  //  =  maximum  intensity  per  unit  length.  Then  the 
meridianal  distribution  of  the  sides  A  +  B  is  : 


FIG.  73. 


7   =  4  r/ 


sn 


+  10°)  +  sin  (0  -  10°)  } 


(28) 


Hereto  in  the  meridian  of  maximum  intensity  is  added  the  light 


LIGHT  FLUX  AND  DISTRIBUTION.  201 

intensity  produced  by  a  half  circle  of  radius  r,  (6);  that  is, 

'2  =  £-'  (29) 

where  I  is  the  circumference  of  the  ellipse  which  projects  the 
circle  of  radius  r,  under  angle  <£,  and  is  given  by  Table  I  and 
Figs.  70  and  71. 


FIG.  74. 

In  the  meridian  of  minimum  intensity,  the  light  intensity  73 
produced  by  the  projection  of  the  half  circle  in  its  own  plane, 
under  angle  (f>,  is  added  to  the  intensity  7t.  This  projection  is, 
by  Fig.  73, 

c  =  r  (1  +  cos  <£),  (30) 

and  thus  73  =  c70' 

=  rIQ'  (1  +  cos  0).  (31) 

In  the  equatorial  plane,  the  intensity,  due  to  the  straight  sides 
A  +  B,  is  constant,  and  is  that  of  a  straight  radiator  under  angle 
10  deg.  from  the  direction  of  maximum  intensity;  hence  is 

70  =  8  rI0'  cos  10°.  (32) 

To  this  is  added  the  intensity  produced  by  the  half  circle  of 
radius  r,  that  is,  72;  hence,  in  the  meridian  of  maximum  intensity, 
7  =  7j  +  72,  Curve  1  of  Fig.  74;  in  the  meridian  of  minimum 


202 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


intensity,  /  =  7X  4-  73,  Curve  2  of  Fig.  74 ;  and  in  the  equator, 
7  =  70  +  72,  Curve  3  of  Fig.  74. 

(8)   In  Table  II  are  recorded  the  intensity  distribution  of  the 
different  radiators  discussed  in  the  preceding  paragraphs. 


TABLE  II. 


Circular  surface. 

Single-loop  filament. 

* 

Rounded  by 

Circular 

Meridian  of 

Plane. 

30  deg. 

60  deg. 

Max. 

intensity. 

Min. 
intensity. 

Equator. 

0 

7.00 

6.50 

5.25 

3.14 

1.70 

1.70 

5.51 

10 

6.88 

6.40 

5.18 

3.12 

1.73 

1.68 

5.50 

20 

6.57 

6.12 

4.94 

3.05 

2.47 

2.35 

5.46 

30 

6.05 

5.63 

4.56 

2.94 

3.19 

2.97 

5.41 

40 

5.35 

4.98 

4.07 

2.78 

3.84 

3.53 

5.33 

50 

4.50 

4.19 

3.55 

2.61 

4.41 

4.02 

5.24 

60 

3.50 

3.25 

3.01 

2.44 

4.88 

4.41 

5.16 

70 

2.39 

2.31 

2.44 

2.24 

5.23 

4.70 

5.06 

80 

1.21 

1.47 

1.90 

2.09 

5.44 

4.88 

4.98 

90 

0 

0.75 

1.37 

2.00 

5.51 

4.94 

4.94 

100 

0.39 

1.00 

110 

0  09 

0  07 

120 

0 

0.04 

130 

0  02 

140 

0  005 

150 

0 

77.  SHADOWS. 

93.  The  radiator  of  an  illuminant  can  rarely  be  arranged  so 
that  no  opaque  bodies  exist  in  its  field  of  light  flux  and  obstruct 
some  light,  that  is,  cast  shadows.  As  the  result  of  shadows,  the 
distribution  of  intensity  of  the  illuminant  differs  more  or  less 
from  that  of  its  radiator,  and  the  total  light  flux  is  less. 

The  most  common  form  of  shadow  is  the  round  shadow  sym- 
metrical with  the  axis  of  the  radiator,  that  is,  the  shadow  of  a 
circular  plane  concentric  with  and  at  right  angles  to  the  sym- 
metry axis  of  the  illuminant.  Such  for  instance  are,  approxi- 
mately, the  shadows  cast  by  the  base  of  the  incandescent  lamp, 
by  the  top  of  the  arc  lamp,  etc.  Such  also  are  the  shadows  of 


LIGHT  FLUX  AND  DISTRIBUTION. 


203 


the  electrodes  in  the  arc  lamp  in  that  most  common  case  where 
the  electrodes  are  in  line  with  each  other. 

As  an  example  may  be  considered  the  effect  of  a  symmetrical 
circular  shadow  on  the  light  flux  and  its  distribution  with  a 
circular  plane  and  with  a  straight  line  as  radiator. 

(1)   Circular  Plane  Opposite  to  Circular  Plane  of  Radiator. 

Shadow  of  negative  carbon  in  front  of  the  positive  carbon 
of  the  carbon  arc. 

In  Fig.  75,  let  2  r  be  the  diameter  of  a  circular  plane  radiator 
(positive  carbon)  ;  2  rl 
the  diameter  of  the 
plane,  which  casts  a 
shadow  (negative  car- 
bon of  the  arc  lamp); 
and  I  the  distance  be- 
tween the  two. 

Assume  70  as  the 
maximum  intensity  of 
the  light  flux  issuing 
from  the  radiator  AOB 
(which  is  in  downward 
direction,  hence  com- 
pletely or  partly  intercepted  by  the  circle  Afl^BJ.  Then,  the 
intensity  of  the  light  flux  from  the  radiator,  in  any  direction  $, 
is,  according  to  reasoning  under  heading  I,  class  (2)  , 

7  =  /0cos0.  (1) 

In  this  direction  <j>,  the  circle  AlBl  projects  on  the  plane  AB 
as  a  circle  A2B2)  with  radius  rv  and  the  center  02  of  this  circle 
has  from  the  center  0  of  the  radiator  the  distance 


FIG.  75. 


a  =  00 


tan 


(2) 


If  now  the  projected  circle  02  overlaps  with  the  radiator  circle 
Ov  the  area  S  of  overlap,  shown  shaded  in  Fig.  76,  is  cut  out  from 
the  radiator  by  the  shadow,  and  the  light  flux  in  the  direction  <j> 
thus  reduced  from  that  of  the  complete  radiator  surface,  Trr2, 
to  that  of  the  radiator  surface  minus  the  shaded  part  S,  that  is, 
xr2-S,  or  in  the  proportion 


2*  -S 


s 


r'x 


(3) 


204  RADIATION,  LIGHT,  AND  ILLUMINATION. 

and  the  intensity  of  the  remaining  light  flux,  in  the  direction  <f>, 
thus  is  I  =  I0q  cos  <£.  (4) 

If  the  distance,  a,  between  the  circles  0  and  02  is  greater  than 
the  sum  of  radii,  I  tan  (j>  >  r  +  r17  the  circles  0  and  02  do  not 
overlap,  and  in  that  direction  no  shadow  is  cast. 

The  light  intensity  thus  is  reduced  by  the  shadow  of  the  lower 
carbon  only  for  those  angles  <j>  which  are  smaller  than  the  angle 

<t>i  given  by  r  +  r 

~--A  (5) 


In  the  direction  in  which  <£  is  smaller  than  the  angle, 

r.  —  r 
tan  ^2  =  ~  —  >  (6) 

and  the  shadow  02  thus  covers  the  entire  radiator  0,  no  light 
issues,  but  the  radiator  is  completely  shaded.  This  can  occur 
only  if  rt>r,  and  if  this  is  the  case,  a  circular  area  below  the 
radiator  receives  no  light. 

If  fj=  r,  the  intensity  becomes  zero  only  in  the  direction 
<j>  =  0;  and  if  7\  <  r,  the  light  in  the  downward  direction  is  merely 
reduced,  but  nowhere  completely  extinguished. 

The  shaded  area  of  the  radiator  consists  of  two  segments, 
of  the  respective  radii  r  and  r1  :  S  =  D  +  Dr 

Let  2  co  =  angle  subtending  segment  D  and  2  co^  =  angle 
subtending  segment  Dv  and  denoting  the  width  of  the  segments 
thus 

w   =  AC, 


and  the  total  width  of  the  shaded  area  is 

p  =  AB2  =  w  +  w,.  (7) 

From  Fig.  76, 

a  =  002   =  OA  +  J~02  -  AB2 

=  r  +  r,  -  p; 
or, 

p  =  r  +  rt  -  a; 
hence,  by  (2), 

p  =  r  +  TI  -  tan  0.  (8) 


LIGHT  FLUX  AND  DISTRIBUTION. 
In  A  02EO, 


205 


sin  < 
sin 

sin  ( 


r   . 
-  sm  aj, 


and 


hence, 


Furthermore, 


S  =  D  +  D, 


and,  by  (3), 


(9) 

(10) 
(ID 

(12) 


(13) 

(14) 
(15) 

(16) 


For  different  values  of  w  the 

values  of  to     wt     p      D      D,     S      q 

are  calculated  from  equations    (10)  (11)  (12)  (13)  (14)  (15)  (16) 
and  then  q  plotted  as  function  of  p  in  Fig.  78. 


206 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


From  equation  (8)  then  follows,  for  every  value  of  <£,  the  cor- 
responding value  of  p,  herefrom  the  value  of  q  and  by  (4)  the 

value  of  /. 


fl 

1.0 

0.9 
0.8 
0.7 
0.6 
0.5 
0.4 
0.3 
0.2 
0.1 
0 

*> 

N 

^ 

N 

^ 

\ 

^ 

\ 

> 

\\s 

^V 

in 

\ 

\ 

\I 

v 

I\ 

\ 

\ 

V 

\n 

P  = 

5 

o 

1     0 

2     0 

3     0 

t     0 

5    0 

6     0 

7    0 

8     0 

^ 

FIG.  78. 


94.  In  Table  III  are  given 
the  values  of  p  and  q  for  the 
ratio  of  radii : 

^-  =  2.0;  1.0;  0.7, 

corresponding  to  a  shadow  sec- 
tion equal  to  4  times,  1  times, 
and  0.5  times  the  section  of  the 
radiator. 

These  are  plotted  as  curves 
I,  II,  III,  in  Fig.  78. 


TABLE  III. 


P' 

r-l=2. 
r 

3-1. 

r 

TI 
r 

=  0.7. 

I. 

II. 

III. 

IV. 

0 

1.000 

1.000 

1.000 

0  96 

0.1 

0.962 

0.964 

0.968 

0.2 

0.885 

0.895 

0.910 

0.3 

0.785 

0.810 

0.835 

0.4 

0.675 

0.715 

0.748 

0.5 
0.6 
0  65 

0.560 
0.435 

0.615 
0.500 

0.660 
0.575 
0  532 

0.660 
0.569 
0  520 

0.7 
0  71 

0.308 

0.380 

0.502 
0  500 

0.477 

0.8 
0.85 

0.183 

0.255 

0.500 

0.386 
0  340 

0.9 

0.070 

0  127 

0  500 

0.95 

0.028 

0  063 

1.0 

0 

0 

0  500 

t 

If  —  <  1,  the  curve  III  represents  the  effective  light-living 

area  only  up  to  the  values  of  p,  where  wl  =  rv  but  beyond  this 
value,  at  least  in  the  application  to  the  shadow  cast  by  the 


LIGHT  FLUX  AND  DISTRIBUTION.  207 

negative  carbon  of  the  arc  lamp,  the  shaded  area  is  not  merely 
the  circle  O/,  but  also  the  area  shown  shaded  in  Fig.  77, 
which  is  shaded  by  the  shadow  cast  by  the  sides  of  the  lower 
electrodes. 

From  the  value  p,  which  corresponds  to  wl  =  rv  the  area  S 
then  increases  by  2^  (p-p)',  hence,  if  S'=  shaded  area  for 
p  =  p'j  for  any  value  of  p>pv 


and  q  =  l ;-         ^j^.  (17) 

XT  nr2 

This  is  shown  in  Table  III  and  in  Fig.  78  as  curve  IV. 

Such  curves  of  intensity  of  a  plane  circular  radiator  of  radius 
r,  shaded  by  a  concentric  circular  shade  of  radius  rl  at  distance  I 
[corresponding  to  a  diameter  of  positive  carbon  2  r,  of  negative 
carbon  2  ri;  and  an  arc  length  Z],  are  given  in  Figs.  79  to  82, 
and  the  numerical  values  given  in  Table  IV. 

r  I 

Fig.  79  gives  the  curves  for  -  =  2,  and  the  arc  lengths,  —  = 

0.25;  0.5;  1.0;  2.0,  as  curves  I,  II,  III,  IV.    Fig.  80  gives  the 

r  2r 

curves  for  -  =  1,  and  the  arc  lengths,  —=  0.25;  0.5;  1.0;  2.0, 

r  I  r 

as  curves  I,  II,  III,  IV.     Fig.  81  gives  the  curves  for  -  =  0.7, 

I  r 

and  the  arc  lengths,  — -  =  0.25;  0.5;  1.0;  2.0,  as  curves  I,  II,  III, 

IV.    In  Fig.  82  are  shown,  for  comparison,  the  intensity  curves 
for 

i-2;      2-r=2'asL 
5-1;       1-1,  as  II. 

^  =  0.7;    ~=0.5,  as  III. 

T  £  T 

As  seen  from  Fig.  82,  a  larger  shade  at  greater  distance,  I, 
gives  approximately  the  same  light  flux  and  a  similar  distribu- 
tion, but  gives  a  much  sharper  edge  of  the  shadow,  while  a  smaller 


208  RADIATION,  LIGHT,  AND  ILLUMINATION. 


V////A  W/\  v////\ 


FIG.  81. 


FIG.  82. 


LIGHT  FLUX  AND  DISTRIBUTION. 


209 


j 

0 

co 

i           b-  t^.  o      i^  o  co      o  10  10      o  co  »o      o  o  »o  o 
»-i  o  o       <o  t^  10       co  o  t-       •*  o  10       o  •<*<  r^  o 

o  »-•  c<i       M  co  ^       >o  «o  eo       r^.  oo  oo       oi  o>  o>  d 

11 

S    3 

II 

0 

•    !        !!          t^.^t"o      co»oo      io»oo      «oo»oo 
O-.          ••            cococo       »o^co       i-io>t^       eoo»oo 

.    I         .    '.           o  i-i  <M       co  •*  »o      «o  <o  t>.      od  o»  o>  d 

I     C 

~l« 

IO 

<M  ^         CO  00  OS         0  •-<  S  0 

fl 

0 

O-                                                                     OT-HCNCO-*»Ot>-oOOSO 

8 

10 

CO 

!!              l!i                                                        !                 03COOOOOOOO 
.      .              .      .      .                                                        .                 CO  IO          Tj<  CO  CM  O 

o 

o    •    •         •    •    •                                     .       o  o  CM       •«*  co  oo  o 

T-H 

o 

t^OlO          O5O5i—  I          t^C<lt--          i—  1  ^f  t-»          OC^C^          COt^-C3i 

(N 

CO  »O  CO         t^  00  OS          00  00  t^          t^  CO  IO          »O  ^  CO          CO  rH  O  O 

H« 

0 

t^-*o       t^coos       -*oot^       ^nrt<t^       o«MTt<       cot^os 

CO^lO          tOCOCO         t^t>»t^         t^CO>O          »O^CO          M  i—  I  O  O 

t>I 

d 

»0 
0 

t^^H-^         cOOSi-H         CO-^iO         i-^CO*O         o<N-rt<         COt^OS 

co-^Tfi       T^T»<»O       loioio       io»oio       iri^co       co»-ioo 

Cl  u 

IO 

co 

10      »o 
t^oso       I-I<MCO      CO<NT-I       ^HOOS      coioco      cot^os 

i? 

o 

COCO'*         -^Tt<Tl<         rt<"*^         -«*<TJ<CO        COCOCO         <M'-"OO 

13 

o 

QOCO         ^OCO         CDOSCO         b-CO-^         OCO(M         OS-*t^ 
i—  I  CO          COOOOO          CO  >—  I  CO          O^ft^          OCMrfrl          »Ot^QO 

a 

II 

CO 

OC^-*          COt>-00          OOOOt^          t^-COO          >OTt<CO          CM»-IOO 

<o_ 
N 

-IS 

O 

COOS          00  t>-  if*          CO  IO  O         t^  CO  -*          O  CO  CO          OS  •«*<  t>- 
O--H          CN(M(M          OCO<M          O^t^          OCN-*          *Ot^OO 

.1 
"3 

*""* 

O>-i<N         COTt<iO         coiOIr^         t^eoiO         lO-^CO        CO»-iC>O 

2 
3 

a 

II 
*TI  v. 

»o 
d 

COOO          -^COOO         t^OO          OO<M          iOCO(M          OS-^t^ 

»0   0             CO   ^H    CO             1-H    CO   rH             T*H   CO   t«-             t-   <M   ^             »0   t>-   00 

OOi-<         »-iCS|<M         COCO-*         -«^-^TJ<         -«t*TjIcO         COi-HOO 

1 

A 

iO 

co 

»O  i—  I          t^»OCO          COOCO          t^COt^.          COt^CO          lO^t» 
CN  >0          1^  0  CO          10  00  0          (N  Tt<  »0         t>-t^t>.          10^.00 

J3 
3 

o 

OOO          O«-l<-l          r-i»-iCN          COCMCO          COCOCO          CO^-iOO 

i 

0 

CO  ^H  -«**         CO  OS  t^         >-irt<l^         0  CO  -«*<         COt^OS 

ii 

CO 

O      -O         O  CO  Tj«         CO  t>-  b,         t^  CO  >O         U5  T*I  CO         CO  ^i  O  O* 

„  1   V- 

IN 

O 

«O  »O  00         O  OS  CO         o  CO  •**         CO  t-  OS 

1—1 

O-                             O         OT-ICO         Tt*^iO         lO-^CO         CO«-«OO 

c4 

11 

•Tl  t- 

.     .          .     .     .          .     .     .                                             -  — 

»o 

CO 

i-i  co      co  t^  o» 

0 

O      •      •            ...            ...            ...         OOO         i-i  ,-H  O  O 

•s 

88JS8Q 

•e- 

o  10  o       »o  o  »o      o  m  o      to  o  »o      o  10  o       10  o  »o  o 

ri          t-HCOCO          COCO-*          ^IO«O          COcOt^          t^OOOOOS 

210          RADIATION,  LIGHT,  AND  ILLUMINATION. 

shade  at  shorter  distance,  III,  gives  a  far  broader  half  shadow, 
which  extends  even  to  the  vertical  direction. 

This  is  illustrated  by  the  distribution  of  the  open  arc  and  the 
enclosed  arc  in  clear  globes  —  that  is,  without  means  of  diffrac- 
tion or  diffusion.  In  the  enclosed  arc  the  distance  between  the 

electrodes,  I,  is  made  larger,  since  the  ratio  of  radii  —  is  greater, 

as  due  to  the  smaller  current  the  diameter  of  the  radiator,  2  r, 
is  smaller  than  in  the  open  arc.  The  enclosed  arc  has  a  much 
sharper  edge  of  the  shadow,  that  is,  narrower  half  shadow,  than 
the  open  arc,  thus  requiring  means  of  diffusion  of  the  light  even 
more  than  the  open  arc. 

Where  the  shade  which  casts  the  shadow  is  rounded,  the  dis- 
tribution curve  is  somewhat  modified  by  similar  considerations, 
as  have  been  discussed  under  headings  I,  class  (4).  This  is  fre- 
quently the  case  where  the  shadow  is  cast  by  the  electrodes  of  an 
arc,  and  especially  so  in  the  carbon  arc,  in  which  the  negative 
electrode  —  which  casts  the  shadow  —  is  more  or  less  rounded 
by  combustion. 

(2)  Circular  Plane  Concentric  with  the  End  of  Linear 
Radiator. 

95.  This  condition  is  approximately  realized  by  the  shadows 
of  the  electrodes  of  a  luminous  arc  with  vertical  electrodes. 

Let,  in  Fig.  83,  2  r1  =  diameter  of  the 
lower  electrode,  I  =  length  of  the  linear- 
radiator,  and  2  w  the  diameter  of  the  radiator. 
Neglecting  first  the  diameter  2  w  of  the  radi- 
ator, the  part  of  the  radiator  which,  in  the 
direction  <£,  is  shaded,  is 

s  =  r,  cot  <£,  (18) 

and  the  reduction  factor  of  the  light,  or  the 
ratio,  by  which  the  intensity  of  light  flux  of 
the  radiator  proper  (heading  I,  class   (5)), 
/  =  70  sin  0,  has  to  be  multiplied,  is 


=   1    -         COt  <£,  (20) 


LIGHT  FLUX  AND  DISTRIBUTION. 


211 


and  the  light  intensity  in  the  direction  <£  thus  is 
/=  qIQ  sin  <J) 

=  /0  ( 1  — j-  cot  (f> J  sin  ^ 

r   /  •  ri 

=  /0  (sin  $  — j  cos 

For  values  of  0  less  than  fa,  where. 


tan 


T 

-1  , 


(21) 


(22) 


the  light  flux  is  zero,  that  is,  complete  shadow  would  exist  if  there 
were  no  diffusion,  etc. 

If  we  now  consider  the  diameter,  2  w,  of  the  radiator,  we  get 
the  same  distribution  of  intensity,  except  in  the  angle 


where  fa'  and  fa'  is  given  by 


tan  fa'  =  -*- 


w 


and       tan  fa"  =  -1— — 

L 


In  this  narrow  angle  the  light  flux  fades  from  the  value  which  it 
has  at  fa"  —  and  which  is  the  same  as  given  by  equation  (21)  — 
to  0  at  fa',  while,  when  neglecting  2w,  the  intensity  would 
become  zero  at  fa  by  equations  (22)  and  (21). 
As  illustrations  are  plotted  in  Fig.  84  and  recorded  in  Table  IV, 


FIG.  84. 


212  RADIATION,  LIGHT,  AND  ILLUMINATION. 

the  distribution  of  light  flux  for—  =0.25;  0.5;  1;  2,  as  curves  I, 

^ri 

II,  III,  IV,  corresponding  to  an  arc  length  equal  to  J,  J,  1  and 
2  times  the  electrode  diameter. 

777.  REFLECTION. 

96.  As  rarely  the  distribution  of  intensity  and  the  brilliancy 
of  the  radiator  are  such  as  desired,  reflection,  diffraction,  and 
diffusion  are  used  to  a  considerable  extent  to  modify  the  distribu- 
tion curve  and  the  brilliancy  of  the  radiator. 

Reflection  may  be  irregular  or  regular  reflection.  In  irregular 
reflection,  the  light  impinging  on  the  reflector  is  thrown  back 
irregularly  in  all  directions,  while  in  regular  reflection  the  light 
is  reflected  under  the  same  angle  under  which  it  impinges  on  the 
reflector.  The  former  is  illustrated  by  a  piece  of  chalk  or  other 
dull  white  body,  the  latter  by  the  mirror. 
A.  Irregular  Reflection. 

Irregular  reflection  is  used  in  indirect  lighting  to  secure  dif- 
fusion and  low  intrinsic  brilliancy  of  the  light  source  by  throw- 
ing the  direct  light  against  the  ceiling  and  illuminating  by  the 
light  reflected  from  white  or  light  colored  ceilings.  In  some 
luminous  arcs,  the  so-called  flame  carbon  arc  lamps,  irregular 
reflection  is  used  to  direct  most  of  the  light  downward  by 
using  a  small  circular  reflector  —  usually  hollow  —  immediately 
above  the  arc,  the  so-called  " economizer."  In  this  case  the 
smoke  produced  by  the  arc  largely  deposits  on  the  reflector 
and  thereby  maintains  it  of  dull  white  color,  the  deposit  of  most 
flame  carbons  being  calcium  fluoride  and  oxide  and  thus  white. 
In  irregular  reflection,  the  reflector  is  a  secondary  radiator; 
that  is,  if  <$!  =  that  part  of  the  flux  of  light  of  the  main  radiator 
which  is  intercepted  by  the  reflector,  and  a  =  albedo  of  the 

reflector  (that  is,  the  ratio  of  reflected 
light  to  impinging  light,  or  the  "ef- 
ficiency of  the  reflector"),  the  radiator 
is  a  generator  of  the  light  flux  a$r 

As  an  example   may  be  discussed 
the  intensity  distribution  of  a  vertical 
FlG-  85-  luminous    arc    L    having   a    circular 

(irregular)  reflector  R  immediately  above  the  arc,  as  shown  in 
Fig.  85.      Let  2  aj  =  angle  subtended  by  the  reflector  R  from 


LIGHT  FLUX  AND  DISTRIBUTION.  213 

the  base  of  the  arc,  I  the  (vertical)  length  of  the  arc.  The 
radius  of  the  reflector  then  is  rl  =  I  tan  co,  and  the  light  flux 
intercepted  by  the  reflector  is  calculated  in  the  manner  as  dis- 
cussed under  heading  II,  Class  (2)  ;  that  is,  if  70  is  the  maximum 
or  horizontal  intensity  of  the  arc  L,  the  intensity  in  the  direc- 
tion (180  deg.  -  <£)  will  be 

7  =  70  sin  <£.  (1) 

The  reflector  then  intercepts  the  entire  light  flux  issuing  from 
the  radiator  L  between  180  deg.  and  180  —  co,  and  the  part  q  of 
the  light  flux  issuing  between  180  —  co  and  90  deg.,  which  is 
given  by 

r,  cot  (180  -  </>)  .A 

q  =  -  -  —  -  —  =  tan  co  cot  <£;  (2) 

i 

hence,  the  light  flux  intensity  which  is  intercepted  by  the  reflec- 
tor is 

A  =  ?/o  sin  * 

=  70  tan  co  cos  <£,  (3) 

and  the  light  intensity  issuing  into  space  from  the  main  radiator 
in  this  angle,  -  <  <£<  (180  -  co),  is 


%  sn 
=  70  (sin  $  —  tan  co  cos  (/>).  (4) 

Therefore  the  light  flux  intercepted  by  the  reflector  within  the 
angle  (f>  =  0  to  ^>  =  co  (or  rather,  <f>  =  180  deg.  to  <f>  =  180  —  co)  is 


within  the  angle  <£  =  &>  to  </>  =  -  is 


$/'  =  2  ^70  /    g  sin2  (j>d(j>  =  2  nI0  tan  o>  /    cos  ^  sin 

I  +  cos  2 


7  sin  2  co 


(5) 


214  RADIATION,  LIGHT,  AND  ILLUMINATION. 

and  therefore  the  total  light  flux  intercepted  by  the  reflector  is 

*1    *    */    +    ^l"    =    <"> 

and  the  reflected  light  flux,  or  light  flux  issuing  from  the  reflector 
as  secondary  radiator,  is 

4>2  =  a^1  =  xIQaco,  (6) 

where  a  =  albedo. 

As  the  reflector  is  a  plane  circular  radiator,  its  maximum 
intensity  is  in  the  downward  direction,  and  is  given  under  head- 
ing I,  class  (2),  as  ^ 

V  =  -  =  /o«",  (7) 

71 

and  herefrom  follows  the  intensity  of  radiation  of  the  secondary 
radiator  in  any  direction  <£, 

r  -  /0"  cos  <£ 

=  70  aw  cos  0.  (8) 

The  total  intensity  of  radiation  of  main  radiator  and  reflector 
or  secondary  radiator  combined,  in  the  lower  hemisphere,  or 

for  0  <  (j>  <  -j  is 

Zi 

/  =  /'  +  /"  =  /o  (gin  0  +  aaj  cos  <£);  (9) 

and  in  the  upper  hemisphere  light  flux  issues  only  under  the 
angle  -  <  $  <  K  —  tu,  and  is 

Zi 

I  =  I'  =  70  (sin  ^  -  tan  w  cos  0).  (10) 


FIG.  86. 

For  to  =  75  deg.  = and  a  =  0.7,  the  intensity  distribution 

12 

is  plotted  in  Fig.  86  and  given  in  Table  V.     The  distribution 


LIGHT  FLUX  AND  DISTRIBUTION. 


215 


curve  is  of  the  type  characteristic  of  most  flame  carbon  arc 
lamps. 
Substituting  the  numerical  values  in 


(9)  gives 
and  in  (10)  gives 


7  =  70  (sin  $  +  0.92  cos 
7  =  70  (sin  $  -  3.73  cos 


TABLE  V. 


Regular:  a  =  0.6. 

<!>. 

Irregular  reflection. 
a  =  0.7. 
<a  =  75  deg. 

Regular  reflection, 
a  =  0.7. 
tal  =  60  deg. 
w2  =  85  deg. 

Irregular:  a'  =  0.1. 
&<!  =  60  deg. 
to2  =  85  deg. 

2r. 
—  1=1. 

I 

0 

3.68 

0 

0.18 

10 

4.32 

0.70 

0.17 

20 

4.83 

1.47 

0.16 

27 

0  16 

30 

5.19 

2.00 

0.42 

35 

0  80 

40 

5.39 

2.57 

1.19 

45 

1  54 

50 

5.44 

3.06 

1.89 

55 

2  23 

60 

5.46 

3.46 

2.55 

65 

4.11 

3  27 

70 

5.02 

4.74 

3.97 

75 

4.82 

5.32 

4.62 

80 

4.58 

5.86 

5.26 

85 

4.30 

6.34 

5.86 

87  5 

5  18 

4  93 

90 

4.00 

4.00 

4.00 

92  5 

2  00 

2  00 

95 

2.68 

0 

0 

100 

1.34 

105 

0 

B.   Regular  Reflection. 

97.  With  regular  reflection  by  a  polished  reflector  or  mirror 
as  used,  for  instance,  in  some  forms  of  luminous  arcs,  the  reflector 
is  represented  by  a  second  radiator,  which  has  the  same  shape  as 
the  main  radiator  and  is  its  image  with  regard  to  the  plane  of  the 
reflector.  If  a  is  the  albedo  of  the  radiator  and  70  the  maximum 


216 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


intensity  of  the  main  radiator,  the  maximum  intensity  of  the 
virtual  or  secondary  radiator  is  a/0. 

The  reflector  then  cuts  out  of  the  light  flux  of  the  radiator 
that  part  intercepted  by  it,  and  adds  to  the  light  flux  that  part 
of  the  (virtual)  light  flux  of  the  secondary  radiator  which  passes 
through  the  plane  of  the  reflector. 

As  example  may  be  considered  the  intensity  distribution  of  a 
vertical  luminous  arc  of  length  Z,  supplied  with  a  circular  ring- 
shaped  mirror  reflector  concentric  with  and  in  the  plane  of  the 
top  of  the  arc.  Let  a)l  be  the  angle  subtended  by  the  inner, 
co2  the  angle  subtended  by  the  outer  edge  of  the  reflector,  from 


FIG.  87. 

the  base  of  the  arc,  as  diagrammatically  illustrated  in  Fig.  87; 
then  the  intensity  of  the  light  flux  of  the  main  radiator 


for 
is 
and  for 

is 

where,  by  (2), 


7  =  70  sin 


7T    - 


hence, 

and  is  zero  for 


q2  =  tan  w2  cot 


cos 


(ID 
(12) 

(13) 
(14) 


7/  =  70  (sin  c/)  —  tan 

(f>   >    7T    -   0)r 

All  the  light  flux  issuing  from  the  main  radiator  between  the 
upper  vertical  and  the  angle  wt  (0  <  <£  <  6^) 

1'  =  70  sin  <f>  (15) 

is  wasted  by  passing  through  the  central  hole  in  the  reflector. 


LIGHT  FLUX  AND  DISTRIBUTION.  217 

Of  the  light  flux  issuing  between  angle  ^  and  -  from  the  upper 

2i 

vertical,  the  part  f  <ut  <  <£  <  -  j 

7,-fc/oSin*  (16) 

is  wasted  by  passing  through  the  hole  in  the  reflector. 
Since,  by  (13), 

ql  =  tan  ^  cot  <£,  (17) 

it  is :  /!  =  70  tan  wt  cos  <£,  (18) 

7T 

for  ^i  <  9  <  o  • 

z 

All  the  light  flux  issuing  between  the  upper  vertical  and  the 
angle  w2, 

7'=70sin<£,  (19) 

is  received  by  the  reflector,  with  the  exception  of  that  part  which 
passes  through  the  hole  in  the  reflector. 

Of  the  light  flux  issuing  between  angle  aj2  and  -  from  the  upper 

Z 

vertical,  the  part 

72=  q2i0sm<j> 
=  IQ  tan  a)2  cos  (j>, 

for*>2<(£<^  (20) 

2i 

is  received  by  the  reflector,  with  the  exception  of  that  part  which 
passes  through  the  hole  in  the  reflector. 

The  total  light  flux  intensity  reflected  by  the  reflector,  or  the 
useful  light  flux  of  the  virtual  or  secondary  radiator,  thus  is,  if 
a  =  albedo  of  the  reflector, 

Within  the  angle  -><£  >  aj2  from  the  upper  vertical, 
2 

7"=  a  (I2  —  7X)  =  aIQ  (tan  co2—  tan  ajj  cos  <£;         (21) 
within  the  angle  a)2  >(f>  >a>l  from  the  upper  vertical, 

I'"  =  a  (P  -  7J  =  «70  (sin  <£  -  tan  ^  cos  <£) ;  (22) 

and  for  ^  >  <£  >  0, 

/""  =  a  (/'  -  7')  =  0;  (23) . 


218  RADIATION,  LIGHT,  AND  ILLUMINATION, 


hence,  the  light  intensity  of  the  illuminant,  consisting  of  vertical 
radiator  and  ring-shaped  mirror  reflector,  for 

0  <  0  <  Wj  is 

7=70sin<£;  (24) 

for  Wj<  <j><  ^2  is 

/=  /'+  i"'  =  /o  { (1  +  a)  sin  <f>  -  a  tan  ^  cos  <£) } ;         (25 


for 


I  =  P  +  I"  =  70  { sin  <j>  +  a  (tan  w2  —  tan  w^  cos  <£ } ;      (26) 


for 

and  for 


7  -=  7/  =  70  (sin  <f>  —  tan  a>2  cos  <£), 

7  =  0. 
17  n 


(27) 


For  ^=  60°  =    ,  ^2  =  85°=  — ,  and  albedo  a=  0.7,  the  in- 

O  OU 

tensity  distribution  is   plotted    in    Fig.   88   and    recorded   in 
Table  V. 


FIG.  88. 

Substituting  the  numerical  values  in  the  foregoing,  we  have: 

(24)  7  =  70sin<£, 

(25)  7  =  70  (1.7  sin  $  -  1.21  cos  <£), 

(26)  7  =  70  (sin  <£  +  6.79  cos  0), 

(27)  7  =  70  (sin  0  -  11.43  cos  <£). 

98.  As  it  is  difficult  to  produce  and  maintain  completely 
regular  reflection,  usually  some  irregular  reflection  is  superim- 
posed upon  the  regular  reflection. 

For  the  irregular  reflection,  the  reflector  is  a  horizontal  plane 
radiator. 


LIGHT  FLUX  AND  DISTRIBUTION.  219 

The  light  flux  reflected  by  a  plane  circular  reflector  subtending 
angles  co1  to  co2,  by  (6),  is 

$.,=  */„  a'  K  L"i),  (28) 

where  a'  is  the  albedo  of  irregular  reflection. 

This  light  flux  gives  in  the  lower  hemisphere  the  maximum 
intensity  for  </>  =  0  as 

7."  -  70a'  (o,2  -  a,,),  (29) 

and  thus  the  intensity  of  the  irregularly  reflected  light  in  the 
direction  <   is 


72  =  /0"  cos 


-  wj  cos  (£,  (30) 


and  this  intensity  thus  adds  to  that  given  by  equations  (24)  to 
(27)  in  the  preceding. 

If  some  light  is  obstructed  by  the  shadow  of  the  lower  elec- 
trode, then  the  light  intensity  of  the  main  radiator,  /',  in  the 

lower  hemisphere  within  the  angle  fa  <  (/>  <  -  >  is  reduced  to 

2 


(31) 
and  becomes  zero  for   </>  <</>,,  where  tan  <£t  ==  y  as  discussed 

I/ 

under  heading  II,  class  (2),  equations  (21),  (22),  where  r{  is  the 
radius  of  the  lower  electrode. 

Thus,  with  a  linear  radiator  of  length  I,  a  diameter  of  the 
lower  electrode  of  2  rv  a  ring-shaped  mirror  reflector  subtending, 
from  the  base  of  the  arc,  the  angles  ^  and  w2,  and  of  the  albedo 
of  regular  reflection  a  and  the  albedo  of  irregular  reflection  a', 
the  light  intensity  distribution  within  is  0  <  (f>  <  (j>v 

I  =  //(^2-  Wl)cos^;  (32) 

within  (f>1  <  (/>  <  Wj  is 

I  =  70  (sin  £+fy  K  -  ^)  --  ^J  cos  ^;  (33) 

within  ^  <  (j>  <  a>2  is 

/  =  /0  (1  +  a)  sin  (/>  +  \a  (co2  -  ^)  -  atan^  -j  lcos(/)|;   (34) 


220  RADIATION,  LIGHT,  AND  ILLUMINATION. 

within  toy  - 


7T  . 

<21S 


Jsin  (j>+\  a  (tan  a)2-  tan  w^)  +  a'  (to2-u^  -  ~ 


cos 


within 
and  within 


I  =  I0  (sin  $  —  tan  a>2  cos  <£), 
K  —  to2  <  </>  <  n  is 
/  =  0. 


(35) 


(36) 


FIG.  89. 

The  distribution  curve  of  such  an  illuminant  is  plotted  in 
Fig.  89  and  recorded  in  Table  V  for  the  values 

^=  60  deg.  =     ;      co2  =  85  deg.  =-r', 


a  =0.60;        a'=  0.10, 


and 


I 


1. 


Substituting  the  numerical  values  in  the  foregoing  equations 
this  gives  ^  =  27  deg. 

(32)  7  =  0.044  70  cos  </>, 

(33)  7  =  70  (sin  <j>  -  0.456  cos  <£), 

(34)  7  =  70  (1.6  sin  <£  -  1.495  cos  <£), 

(35)  7  =  70  (sin  <j>  +  5.364  cos  <£), 

(36)  7  =  70  (sin  <j>  -  11.43  cos  <j>). 


FIG.  90. 

As  comparison  is  given  in  Fig.  90  the  distribution  curve  of 
the  magnetite  arc,  which  is  designed  of  the  type  of  Fig.  89 
for  the  purpose  of  giving  more  nearly  uniform  illumination  in 
street  lighting. 


LIGHT  FLUX  AND  DISTRIBUTION.  221 

IV.    DIFFRACTION,  DIFFUSION,  AND  REFRACTION. 

99.  Many  radiators  are  of  too  high  a  brilliancy  to  permit 
their  use  directly  in  the  field  of  vision  when  reasonably  good 
illumination  is  desired.  A  reduction  of  the  brilliancy  of  the 
illuminant  by  increasing  the  size  of  the  virtual  radiator  thus 
becomes  necessary.  This  is  accomplished  by  surrounding  the 
radiator  by  a  diffracting,  diffusing,  or  prismatically  refracting 
envelope. 

Diffraction  is  given  by  a  frosted  glass  envelope,  as  a  sand 
blasted  or  etched  globe;  diffusion  by  an  opal  or  milk-glass 
globe.  The  nature  of  both  phenomena  is  different  to  a  consider- 
able extent,  and  a  frosted  globe  and  an  opal  globe  thus  are  not 
equivalent  in  their  action  on  the  distribution  of  the  light  flux. 
This  may  be  illustrated  by  Fig.  91. 

Let,  in  Fig.  91,  1A,  R  represent  the  light-giving  radiator, 
for  simplicity  assumed  as  a  point,  and  G  represent  a  diffracting 
sheet,  as  a  plate  of  ground  glass.  A  beam  of  light,  C,  issuing 
from  the  radiator  R  is,  in  traversing  the  diffracting  sheet  G, 
scattered  over  an  angle,  that  is,  issues  as  a  bundle  of  beams  D} 
of  approximately  equal  intensity  in  the  middle  and  fading  at 
the  edges '.  The  direction  of  the  scattered  beam  of  light  D,  that 
is,  its  center  line,  is  the  same  as  the  direction  of  the  impinging 
beam  C,  irrespective  of  the  angle  made  by  the  diffracting  sheet 
with  the  direction  of  the  beam. 

Different  is  the  effect  of  diffusion,  as  by  a  sheet  of  opal  glass, 
shown  as  G  in  Fig.  91,  IB.  Here  the  main  beam  of  light  G 
passes  through,  as  C',  without  scattering  or  change  of  direction, 
but  with  very  greatly  reduced  intensity;  usually  also  with  a 
change  of  color  to  dull  red,  due  to  the  greater  transparency  of 
opal  glass  for  long  waves.  Most  of  the  light,  however,  is  irregu- 
larly reflected  in  the  opal  glass,  and  the  point  or  area  at  which 
the  beam  C  strikes  the  sheet  G  becomes  a  secondary  radiator 
and  radiates  the  light  with  a  distribution  curve  corresponding 
to  the  shape  of  (2,  that  is,  with  a  maximum  intensity  at  right 
angles  to  the  plane  of  G,  as  illustrated  in  Fig.  91,  1  B. 

A  point  P  thus  receives  from  a  radiator  R,  enclosed  by  a  diffract- 
ing globe  G,  a  pencil  of  light,  as  shown  in  Fig.  91,  2  A,  and  from 
the  point  P  the  radiator  appears  as  a  ball  of  light,  shown  densely 
shaded  in  3  A,  surrounded  by  a  narrow  zone  of  half  light, 


222 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


shown  lightly  shaded,  and  in  the  interior  of  a  non-luminous  or 
faintly  luminous  envelope. 

If  the  radiator  R  is  enclosed  by  a  diffusing  globe,  Fig.  91,  B2, 
the  point  P  receives  light  from  all  points  of  the  envelope  G  as 


FIG.  91. 


3-B 


secondary  radiator,  and  a  ray  of  direct  light  from  the  radiator  R. 
From  the  point  P  the  entire  globe  G  thus  appears  luminous,  and 
through  it  shows  faintly  the  radiating  point  R,  as  sketched  in 
3B. 

An  incandescent-lamp  filament  in  an  opal  globe  thus  is  clearly 


LIGHT  FLUX  AND  DISTRIBUTION. 


223 


but  faintly  visible,  surrounded  by  a  brightly  luminous  globe, 
while  an  incandescent  filament  in  a  frosted  globe  appears  as  a 
ball  of  light  surrounded  by  a  non-luminous  or  faintly  luminous 
globe,  but  the  outline  of  the  filament  is  not  visible. 

100.  The  distribution  of  light  flux  thus  essentially  depends 
on  the  shape  of  the  diffusing  envelope,  but  does  not  much  depend 
on  the  shape  of  the  diffracting  envelope;  that  is,  a  diffracting 
envelope  leaves  the  distribution  curve  of  the  radiator  essentially 
unchanged,  and  merely  smooths  it  out  by  averaging  the  light  flux 
over  a  narrow  range  of  angles,  while  a  diffusing  envelope  entirely 
changes  the  distribution  curve  by  substituting  the  diffusing  globe 
as  secondary  radiator,  and  leaves  only  for  a  small  part  of  the  light 
-  that  of  the  direct  beam  C'  —  the  intensity  distribution  of  the 
primary  radiator  unchanged. 

Thus,  for  a  straight  vertical  cylindrical  envelope  surrounding 
a  radiator  giving  the  distribution  curve  shown  in  Fig.  92,  curve  I, 


FIG.  92. 

the  distribution  curve  is  changed  by  diffraction  (frosted  en- 
velope), to  that  shown  in  Fig.  92,  curve  II,  but  changed  to  that 
shown  by  Fig.  92,  curve  III,  by  diffusion  (opal  envelope).  The 
latter  consists  of  a  curve  due  to  the  transmitted  light  and  of  the 
same  shape  as  I,  and  a  curve  due  to  the  diffused  light,  or  light 
coming  from  the  envelope  as  secondary  radiator.  The  latter  is 
the  distribution  curve  of  a  vertical  cylindrical  radiator,  as  dis- 
cussed under  heading  I,  class  (5). 
The  shape  of  a  diffusing  envelope  thus  is  of  essential  importance 


224 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


for  the  distribution  of  the  light  intensity,  while  the  shape  of  the 
diffracting  envelope  is  of  less  importance. 


TABLE  VI. 


f. 

v 

Clear  globe. 

v 

Frosted  globe. 

V 

Opal  globe. 

n 

5 

U 

in 

5 

1U 

20 

6 

8 

11 

2*5 

7 

12 

m9 

30 

9 

18 

17 

35 

15 

26 

40 

34 

35 

25 

45 

49.6 

43 

50 

50.6 

47.5 

32 

55 

49.6 

48 

60 

47.5 

46 

34.5 

fi7 

43 

42 

U  1 

70 

37 

37 

35 

75 

29 

32 

80 

20 

26 

34 

85 

15 

21 

90 

13.5 

17 

32 

95 

13 

14 

100 

12.5 

13 

30.5 

110 

12 

12 

29.5 

120 

11 

11 

27 

130 

9 

9 

24 

140 

6 

7 

20 

150 

0 

2 

15 

160 

0 

0 

10 

It  is  obvious  that  frosted  glass  does  not  perfectly  represent 
diffraction,  but  some  diffusion  occurs,  especially  if  the  frosting 
is  due  to  etching,  less  if  due  to  sand-blasting.  Opal  glass  also 
does  not  give  perfect  diffusion,  but,  in  the  secondary  radiation 
issuing  from  it,  the  direction  of  the  horizontal  or  impinging  beam 
slightly  preponderates. 

101.  Regular  or  prismatic  refraction  also  affords  a  means  of 
decreasing  the  brilliancy  by  increasing  the  size  of  the  virtual 
illummant,  and  at  the  same  time  permits  the  control  of  the 


LIGHT  FLUX  AND  DISTRIBUTION. 


225 


intensity  distribution.  It  probably  is  the  most  efficient  way, 
as  involving  the  least  percentage  of  loss  of  light  flux  by  absorp- 
tion. 

For  instance,  by  surrounding  the  radiator  R  by  a  cylindrical 
lens,  as  shown  diagrammatically  in  Fig.  93,  the  rays  of  light  may 


^ 


FIG.  93. 

be  directed  into  the  horizontal  (or  any  other  desired)  direction, 
and  the  entire  lens  then  appears  luminous,  as  virtual  radiator. 

Usually  in  this  case,  instead  of  a  complete  lens,  individual  sec- 
tions thereof  are  used,  as  prisms,  as  shown  in  Fig.  94,  and  this 


FIG.  94. 

method  of  light  control  thus  called  "prismatic  refraction,"  or, 
where  the  light  does  not  pass  through,  but  is  reflected  and  turned 
back  from  the  back  of  the  prism,  "prismatic  reflection." 

Such  prismatically  reflecting  or  refracting  envelopes  and  shades 
have  found  an  extensive  use. 


LECTURE   XI. 
LIGHT   INTENSITY  AND   ILLUMINATION. 

A.   INTENSITY  CURVES  FOR  UNIFORM 
ILLUMINATION. 

102.  The  distribution  of  the  light  flux  in  space,  and  thus  the 
illumination,  depends  on  the  location  of  the  light  sources,  and  on 
their  distribution  curves.  The  character  of  the  required  illumi- 
nation depends  on  the  purpose  for  which  it  is  used:  a  general 
illumination  of  low  and  approximately  uniform  intensity  for  street 
lighting;  a  general  illumination  of  uniform  high  intensity  in 
meeting  rooms,  etc.;  a  local  illumination  of  fairly  high  intensity 
at  the  reading-table,  work  bench,  etc.  ;  or  combinations  thereof, 
as,  in  domestic  lighting,  a  general  illumination  of  moderate  inten- 
sity, combined  with  a  local  illumination  of  high  intensity.  Even 
the  local  illumination,  however,  within  the  illuminated  area 
usually  should  be  as  uniform  as  possible,  and  the  study  of  the 
requirements  for  producing  uniformity  of  illumination  either 
throughout  or  over  a  limited  area  thus  is  one  of  the  main  prob- 
lems of  illuminating  engineering. 

The  total  intensity  of  illumination,  i,  at  any  point  in  space  is 
proportional  to  the  light  intensity,  7,  of  the  beam  reaching  this 
point,  and  inversely  proportional  to  the  square  of  the  distance 
I  of  the  point  from  the  effective  center  of  the  light  source  : 


If  the  beam  of  light  makes  the  angle  <f>  with  the  vertical 
direction,  the  illumination,  i,  is  thus  in  the  direction  <j>,  the 
horizontal  illumination,  that  is,  the  illumination  of  a  horizontal 
plane  (as  the  surface  of  a  table),  is 

,       7cos<  , 

ih  =  i  cos  0  = 


226 


LIGHT  INTENSITY  AND  ILLUMINATION.  227 

and  the  vertical  illumination,  that  is,  the  illumination  of  a  vertical 
plane  (as  the  sides  of  a  room),  is 

7  sin  0 
iv  =  i  sin  <£  =  — —!-  •,  (3) 

If,  then,  in  Fig.  95,  L  is  a  light  source  at  a  distance  lv  above 
a  horizontal  plane  P,  then,  for  a  point  A  at  the  horizontal  dis- 


FIG.  95. 


tance  lh  from  the  lamp,  L  (that  is,  the  distance  lh  from  the  point 
B  of  the  plane  P,  vertically  below  the  lamp  L),  we  have: 


, 

Lv 

and  the  distance  of  the  point  A  from  the  light  is 


cos 


hence,  the  total  illumination  at  point  A  is 

.      7  cos2  ()  . 


the  horizontal  illumination  is 


l 


7  cos 


and  the  vertical  illumination  is 

.       7  cos2  <f>  sin 


(4) 
(5) 

(6) 
(7) 
(8) 


where  7  is  the  intensity  of  the  light   source   in   the   direc- 
tion <j>. 

Inversely,  to  produce  a  uniform  total  illumination,  i0,  on  the 


228  RADIATION,  LIGHT,  AND  ILLUMINATION. 

horizontal  plane  P,  the  intensity  of  the  light  source  must  vary 
with  the  angle  </>  according  to  the  equation  (6) : 

7"  1 2 

(9) 

or,  if  we  denote  by  70  the  vertical,  or  downward,  intensity  of 
the  light  source, 

A,  -  V,2;  (10) 

hence, 

7  =  ^-  (11) 

gives  the  intensity  distribution  of  the  light  source  required  to 
produce  uniform  total  illumination  i0  on  a  horizontal  plane  be- 
neath the  light. 

In  the  same  manner  follows  from  (7)  and  (8) : 

To  produce  uniform  horizontal  illumination  ihQ  on  a  plane  P 
beneath  the  light  source  L,  the  intensity  curve  of  the  light  source 
is  given  by 

cos3  </> 

and,  to  produce  uniform  vertical  illumination  iVQ  of  objects  in 
the  plane  P  beneath  the  light  source  L, 

7-          /0  (13) 


cos"  <p  sin  0 

Where  the  objects  in  the  plane  P  which  are  to  be  illuminated 
may  have  different  shapes — as  on  a  dining-table,  work  bench, 
etc.,  uniformity  of  the  total  illumination,  i,  is  desirable;  where 
all  the  objects  which  shall  be  illuminated  are  horizontal — as 
the  surface  of  a  drafting-board  — constancy  of  the  horizontal 
illumination  ih  is  desirable,  while  where  vertical  objects  are  to  be 
illuminated  — as,  for  instance,  to  read  labels  on  bottles  — con- 
stancy of  the  vertical  illumination  iv  is  desirable. 

By  "horizontal  illumination"  ih  is  here  understood  the  illumi- 
nation of  a  horizontal  plane,  which  is  due  to  the  vertical  compo- 
nent of  the  total  light  flux,  while  the  "vertical  illumination " 
iv  is  the  illumination  of  a  vertical  plane,  due  to  the  horizontal 
component  of  the  light  flux. 


LIGHT  INTENSITY  AND  ILLUMINATION. 


229 


In  Fig.  96,  the  intensity  curves  of  the  light  source  required 
to  give  uniform  total  illumination  i0  (11)  in  a  horizontal  plane 
are  plotted  as  curves  I,  II  and  III;  the  intensity  distribution 
for  uniform  horizontal  illumination  iho  (12)  is  plotted  as  curve 
IV,  and  the  intensity  distribution  for  uniform  vertical  illumina- 
tion iVQ  (13)  in  the  horizontal  plane  beneath  the  light  source 
is  plotted  as  curve  V.  For  convenience,  curves  IV  and  V  are 
shown  in  the  upper  half  of  the  diagram.  The  numerical  values 
for  lv  =  1  are  recorded  in  Table  I.  With  increasing  angle  $, 
the  required  intensity  increases  very  rapidly,  and,  as  is  obvious, 
becomes  infinite  for  (f>  =  90  deg. 

TABLE    I.— (Figs.    95    and    96.) 
UNIFORM  DISTRIBUTION   ILLUMINATION  CURVES. 


f. 

COS   (p. 

Total. 

1 

Horizontal. 
1 

Vertical. 
1 

degrees. 

cos2  <f> 

cos3  <j> 

sin  ^  cos2  <f> 

0 

1 

1 

1 

00 

5 

996 

1.01 

1.015 

11.60 

10 

985 

1.03 

1.045 

5.90 

15 

966 

.07 

1.11 

4.30 

20 

940 

.13 

1.20 

3.30 

25 

906 

.22 

1.35 

2.88 

30 

866 

.33 

1.54 

2.66 

35 

819 

.49 

1.82 

2.59 

40 

766 

.70 

2.22 

2.64 

45 

707 

2.00 

2.83 

2.83 

50 

643 

2.43 

3.73 

3.17 

55 

574 

3.03 

5.27 

3.70 

60 

500 

4.00 

8.00 

4.60 

65 

423 

5.59 

13.20 

6.16 

70 

342 

8.35 

24.4 

8.90 

75 

259 

15.10 

58.3 

15.60 

80 

174 

33.00 

190.0 

32.50 

85 

087 

132.00 

152.0 

133.00 

90 

0 

00 

00 

00 

103.  Therefore,  in  the  problem,  as  it  is  usually  met,  of  pro- 
ducing uniform  intensity  i0  over  a  limited  area,  subtending  angle 
2  aj  beneath  the  light  source,  the  intensity  of  the  light  source 


230          RADIATION,  LIGHT,  AND  ILLUMINATION. 


FIG.  96. 


FIG.  97, 


LIGHT  INTENSITY  AND  ILLUMINATION.  231 

should  follow  (11)  for  0  <  <f>  <  a>.  Beyond  <£  =  a>,  the  intensity 
may  rapidly  decrease  to  zero  —  as  would  be  most  economical,  if 
no  light  is  required  beyond  the  area  subtended  by  angle  2  co. 
This,  for  instance,  is  the  case  with  the  concentrated  lighting  of  a 
table,  etc.  However,  the  intensity  beyond  (f>  =  to  may  follow  a 
different  curve,  to  satisfy  some  other  requirements,  for  instance, 
to  produce  uniform  illumination  in  a  vertical  plane.  Thus  in 
domestic  lighting,  for  the  general  uniform  illumination  of  a  room 
by  a  single  illuminant,  the  intensity  curve  would  follow  equation 
(11)  up  to  the  angle  a>  — if  2  w  is  the  angle  subtended  by  the  floor 
of  the  room  from  the  light  source  —  and  for  $  >  cu  the  intensity 
curve  would  follow  the  equation, 

/  =   -4-r,  (14) 

sin2  <j> 

which  gives  uniform  illumination  in  the  vertical  plane,  that  is,  of 
the  walls  of  the  room. 

In  Fig.  98  are  shown  intensity  curves  of  a  light  source  giving 
uniform  illumination  in  the  horizontal  plane  beneath  the  lamp, 
from  0  to  CD,  and  the  same  uniform  illumination  in  the  vertical 
plane  from  $  =  a>  to  <j>  =  90  deg.,  as  diagrammatically  shown  in 
Fig.  97;  that  is,  uniform  illumination  of  the  floor  of  a  room 
and  (approximately)  its  walls,  by  a  lamp  located  in  the  center 
of  the  ceiling,  where  cu  is  the  (average)  angle  between  the 
vertical  and  the  direction  from  the  lamp  to  the  edge  of  the 
floor: 

I  for  co  =  30  deg.;  or  diameter  of  floor  -f-  height  of  walls  = 

2 
2  tan  30  deg.  =  —==1.15. 

II  for  co  =  45  deg.;  or  diameter  of  floor  -j-  height  of  walls  = 

2  tan  45  deg.  =  2. 

III  for  aj  =  60  deg.;  or  diameter  of  floor  -H  height  of  walls  = 

2  tan  60  deg.  =  2  V3  =  3.46. 

IV  for  a)  =  75  deg.;  or  diameter  of  floor  -f-  height  of  walls  = 

2  tan  75  deg.  =  7.46. 

These  curves  are  drawn  for  the  same  total  flux  of  light  in  the 
lower  hemisphere,  namely,  250  mean  hemispherical  candle  power; 


232          RADIATION,  LIGHT,  AND  ILLUMINATION. 

or,  1570  lumens.    The  vertical  or  downward  intensities  70  are 
in  this  case: 

I:  aj  =  30  deg.;  70  =  428  cp. 

II:  cu  =  45  deg.;  70  =  195  cp. 
Ill:  w  =  60  deg.;  70  =  95  cp. 
IV:  aj  =  75  deg.;  70  =  41.5  cp. 

The  values  are  recorded  in  Table  II,  in  column  I,  for  equal 
downward  candle  power  70,  and  in  column  a,  for  equal  light  flux, 
corresponding  to  1  mean  hemispherical  candle  power. 

TABLE  II.  —  (Figs.  97  to  99.)     INTENSITY  CURVES. 

Uniform  illumination  from  vertical  <t>  =  0  to  <f>  =  «  degrees  from  verti- 
cal, and 

(a)  Uniform  illumination  (on  vertical  plane)  from  <f>  =  w  to  horizontal 
0  =  90  deg. 

(6)  No  illumination  beyond  <J>  =  w. 

70  for  unity  illumination  at  0  =  0. 

a  and  6  for  mean  hemispherical  candle  power  1,  or  2  TT  lumens. 


<j>. 

ca  =  30  deg. 

w  =  45  deg. 

a>  =  60  deg. 

to  =  75  deg. 

/0< 

a. 

6. 

V 

a. 

b. 

V 

a. 

b. 

I0- 

a. 

6. 

0 
5 
10 

.00 
.01 
1.03 

1.71 
1.72 
1.76 

3.73 
3.76 
3.83 

1.00 
1.01 
1.03 

0.78 
0.79 
0.80 

1.57 
1.58 
1.62 

1.00 
1.01 
1.03 

0.38 
0.385 
0.39 

0.67 
0.67 
0.685 

1.00 
1.01 
1.03 

0.166 
0.168 
0.172 

0.222 
0.224 
0.229 

15 
20 
25 

.07 
.13 
.17 

1.83 
1.93 
2.00 

3.98 
4.20 
4.35 

1.07 
1.13 
1.22 

0.83 
0.88 
0.95 

1.68 
1.77 
1.99 

1.07 
1.13 
1.22 

0.41 
0.43 
0.465 

0.71 
0.75 
0.81 

1.07 
1.13 
1.22 

0.178 
0.188 
0.203 

0.237 
0.251 
0.271 

30 
35 
40 

1.20 
1.01 
0.81 

2.05 
1.73 
1.38 

4.47 
3.57 
2.24 

1.33 
1.49 
1.70 

1.03 
1.16 
1.32 

2.08 
2.33 
2.66 

1.33 
1.49 
1.70 

0.51 
0.57 
0.65 

0.89 
0.99 
1.13 

1.33 
1.49 
1.70 

0.221 
0.248 
0.283 

0.295 
0.331 
0.377 

45 
50 
55 

0.67 
0.57 
0.50 

1.14 
0.98 
0.85 

0.57 
0 

1.80 
1.70 
1.49 

1.40 
1.32 
1.16 

2.85 
2.50 
1.10 

2.00 
2.43 
3.03 

0.76 
0.93 
1.16 

1.34 
1.62 
2.02 

2.00 
2.43 
3.03 

0.333 
0.405 
0.504 

0.445 
0.540 
0.672 

60 
65 
70 

0.44 
0.41 
0.38 

0.75 
0.70 
0.65 

1.33 
1.22 
1.13 

1.03 
0.95 
0.88 

0.31 
0 

3.60 
3.51 
3.39 

1.37 
1.34 
1.29 

2.40 
2.00 
0.80 

4.00 
5.59 
8.35 

0.665 
0.930 
1.39 

0.887 
1.24 
1.86 

75 
80 
85 

0.36 
0.34 
0.34 

0.61 
0.58 
0.58 



1.07 
1.03 
1.01 

0.83 
0.80 
0.79 

3.21 
3.09 
3.03 

1.22 

1.18 
1.16 

0.20 
0 

12.80 
12.40 
12.10 

2.13 
2.07 
2.02 

2.85 
2.11 
0.67 



90 

0.33 

0.57 

1.00 

0.78 

3.00 

1.14 

12.00 

2.00 

0.11 

LIGHT  INTENSITY  AND  ILLUMINATION. 


233 


These  curves  in  Fig.  98  consist  of  a  middle  branch,  giving  uni- 
form floor  illumination,  and  two  side  branches,  giving  uniform 
side  illumination,  and  are  rounded  off  where  the  branches  join. 


FIG.  98. 


Fig.  99  gives  the  intensity  curves  for  the  same  angles,  w  =  30, 
45,  60,  and  75  deg.,  for  uniform  illumination  only  in  the  hori- 


FIG.  99. 


zontal  plane  beneath  the  lamp,  but  no  illumination  beyond 
this;  for  <£  >  a>,  the  light  flux  rapidly  decreases. 

The  curves  in  Fig.  99  are  also  plotted  for  equal  total  light  flux, 
of  150  mean  hemispherical  candle  power,  or  940  lumens.     The 


234          RADIATION,  LIGHT,  AND  ILLUMINATION. 

curve,  0,  giving  (approximately)  uniform  illumination  within  an 
angle  of  20  deg.,  or  for  a>  =  10  deg.,  is  added  to  the  set;  this  curve, 
however,  is  plotted  for  one-tenth  the  light  flux  of  the  other 
curves,  94  lumens,  or  15  mean  hemispherical  candle  power. 

The  vertical  or  downward  intensities  70  are  in  this  case,  for 
equal  light  flux  of  940  lumens : 

I:  'a>  =  30  deg.;  70  =  500  cp. 
II:  a)  =  45  deg.;  70  =  235  cp. 
Ill:  co  =  60  deg.;  70  =  100  cp. 
IV:  aj  =  75  deg.;  70  =  25  cp. 
0:  aj  =  10  deg.;  70  =  7000  cp. 

Fig.  99  best  illustrates  the  misleading  nature  of  the  polar  dia- 
gram of  light  intensities.  It  is  hard  to  realize  from  the  appearance 
of  Fig.  99  that  curves  I,  II,  III  and  IV  represent  the  same  light 
flux,  and  curve  0  one-tenth  the  light  flux,  that  is,  little  more 
than  half  the  light  flux  of  a  16-cp.  lamp. 

Curve  0,  however,  illustrates  that  enormous  light  intensities 
can  be  produced  with  very  little  light  flux,  if  the  light  flux  is 
concentrated  into  a  sufficiently  narrow  beam.  This  explains 
the  enormous  light  intensities  given  by  search-light  beams:  for 
oj  =  1  deg.,  or  a  concentration  of  the  light  flux  into  an  angle  of 
2  deg.  —  which  is  about  the  angle  of  divergency  of  the  beam  of  a 
good  search  light  —we  would  get  7  =  700,000  cp.  in  the  beam, 
with  15  mean  hemispherical,  or  7.5  mean  spherical,  candle  power 
light  source;  and  a  light  source  of  9000  mean  spherical  candle 
power  —a  160-ampere  60- volt  arc  —would  thus,  when  concen- 
trated into  a  search-light  beam  of  2  deg.,  have  an  intensity  in  the 
beam  of  70  =  210  million  candle  power,  when  allowing  75  per  cent 
loss  of  light  flux,  that  is,  assuming  that  only  25  per  cent  of  the 
light  flux  is  concentrated  in  the  beam. 

The  numerical  values  of  Fig.  99  are  given  as  b  in  Table  II,  for 
equal  light  flux  corresponding  to  1  mean  spherical  candle  power. 

B.  STREET  ILLUMINATION  BY  ARCS. 

104.  To  produce  uniform  illumination  in  a  plane  beneath 
the  illuminant,  a  certain  intensity  distribution  curve  is  required, 
as  discussed  in  A ;  for  other  problems  of  illumination,  correspond- 
ingly different  intensity  curves  would  be  needed  to  give  the 
desired  illumination. 


LIGHT  INTENSITY  AND  ILLUMINATION.  235 

It  is  not  feasible  to  produce  economically  any  desired  distribu- 
tion curve  of  a  given  illuminant.  Therefore,  the  problem  of 
illuminating  engineering  is  to  determine,  from  the  purpose  for 
which  the  illumination  is  used,  the  required  distribution  of  illu- 
mination, and  herefrom  derive  the  intensity  curve  of  the  illumi- 
nant which  would  give  this  illumination.  Then  from  the  existing 
industrial  illuminants,  or  rather  from  those  which  are  available 
for  the  particular  purpose,  that  is  selected  whose  intensity  dis- 
tribution curve  approaches  nearest  to  the  requirements,  and 
from  the  actual  intensity  curve  of  this  illuminant  the  illumination 
which  it  would  give  is  calculated,  so  as  to  determine  how  near  it 
fulfils  the  requirements. 

The  intensity  curve  of  the  illuminant,  required  to  give  the 
desired  illumination,  depends  on  the  location  of  the  illuminant 
and  the  number  of  illuminants  used.  Thus  if,  with  a  chosen 
location  and  number  of  light  sources,  no  industrial  illuminant 
can  be  found  which  approaches  the  desired  intensity  curve 
sufficiently  to  give  a  fair  approach  to  the  desired  illumination, 
a  different  location,  or  different  number  of  light  sources  would 
have  to  be  tried.  Here,  as  in  all  engineering  designs  which 
involve  a  large  number  of  independent  variables,  judgment 
based  on  experience  must  guide  the  selection.  If  so,  practically 
always  some  industrially  available  illuminant  can  be  found 
which  sufficiently  approaches  the  intensity  curve  required  by 
the  desired  illumination. 

As  example  may  be  discussed  the  problem  of  street  lighting. 

This  problem  is :  with  a  minimum  expenditure  of  light  flux- 
that  is,  at  minimum  cost  — to  produce  over  the  entire  street  a 
sufficient  illumination.  This  illumination  may  be  fairly  low, 
and  must  be  low,  for  economic  reasons,  where  many  miles  of 
streets  in  sparsely  settled  districts  have  to  be  illuminated. 
This  requires  as  nearly  uniform  illumination  as  possible,  since 
the  minimum  illumination  must  be  sufficient  to  see  by,  and  any 
excess  above  this  represents  not  only  a  waste  of  light  flux,  but, 
if  the  excess  is  great,  it  reduces  the  effectiveness  of  the  illumina- 
tion at  the  places,  where  the  intensity  is  lower,  by  the  glare  of 
the  spots  of  high  illumination. 

Uniformity  of  street  illumination  thus  is  of  special  importance 
where  the  illumination  must  for  economic  reasons  be  low;  while 
in  the  centers  of  large  cities,  or  in  densely  populated  districts, 


236 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


as  European  cities,  the  relatively  small  mileage  of  streets  per 
thousand  inhabitants  economically  permits  the  use  of  far  greater 
light  fluxes,  and  then  uniformity,  while  still  desirable,  becomes 

less  essential. 

TABLE  III  —  (Figs   100  and  101.) 


Intensity:  100  m.  sph.  cp. 

Illumination:  200  m.  sph.  cp.;  /„  =  20. 

a. 

6. 

c. 

a. 

6. 

c. 

1 

D.  C. 

D.  C. 

D.  C. 

D.  C. 

«c 

enclosed 

enclosed 

Magnetite 

Distance. 

enclosed 

enclosed 

Magnetite 

carbon 

carbon 

arc. 

carbon 

carbon 

arc. 

arc. 

arc. 

Clear 

arc. 

arc.  . 

Clear 

Clear  inner 

Opal  inner 

globe. 

Clear  inner 

Opal  inner 

globe. 

globe. 

globe. 

globe. 

globe. 

4>. 

7. 

7. 

7. 

x  =  -• 

i. 

i. 

t. 

h 

0 

30 

45 

59 

0 

15 

22.5 

29.5X10~3 

10 

42 

50 

63 

0.2 

22 

24.5 

30.5 

20 

92 

70 

69 

0.4 

46 

33.0 

31.0 

30 

182 

107 

79 

0.6 

73 

42.5 

31.0 

40 

247 

150 

102 

0.8 

73 

44.5 

30.5 

45 

270 

1.0 

67 

40.5 

29.5 

50 

257 

171 

136 

1.2 

53 

35.5 

28.0 

60 

210 

181 

177 

1.4 

39 

30.5 

26.0 

70 

147 

182 

226 

1.6 

30.5 

25.5 

23.5 

75 

122 

181 

243 

1.8 

24.5 

21.5 

21.5 

80 

97 

160 

250 

2.0 

19.0 

18.0 

19.0 

85 

75 

118 

249 

2.5 

11.5 

13.0 

15.0 

90 

65 

89 

197 

3.0 

7.0 

9.5 

12.0 

100 

57 

82 

47 

3.5 

5.0 

7.0 

9.5 

110 

57 

77 

16 

4.0 

3.5 

5.5 

7.5 

120 

60 

68 

5.0 

2.0 

3.2 

4.8 

130 

35 

62 

6.0 

1.2 

2.0 

3.4 

140 

3 

56 

7.0 

1.0 

1.4 

2.5 

150 

17 

8.0 

0.8 

1  .0 

2.0 

9.0 

0.5 

0.8 

1.7 

10.0 

0.4 

0.6 

1  1 

15.0 

0.2 

0.3 

0.5 

20.0 

0.  1 

0.  1 

0.3 

25^0 

0.1 

Q.I 

0^2 

The  arc,  as  the  most  economical  illuminant,  is  mostly  used 
for  street  lighting.     Fig.  100  gives  the  average  intensity  curves 


LIGHT  INTENSITY  AND  ILLUMINATION. 


237 


of  three  typical  arcs  for  equal  light  flux  of  200  mean  spherical 
candle  power: 


FIG.  100. 


I.  The  direct-current  enclosed  carbon  arc,  with  clear  inner 
globe:  a  curve  of  the  character  discussed  in  Fig.  82.  II.  The 
direct-current  enclosed  carbon  arc,  with  opal  inner  globe:  a 


0:20 


III 


1,60 


1,00 


0.4  0,2 


08  0,4  06  08  10  12  It  16  18  20  22  24  26  28 


FIG.  101. 


curve  of  the  character  discussed  in  Fig.  92.  III.  The  magnetite 
arc  or  luminous  arc,  with  clear  globe:  a  curve  of  the  character 
discussed  in  Fig.  89.  The  numerical  values  are  recorded  in 
Table  III,  per  100  mean  spherical  candle  power. 


238 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


Herefrom  then  follows,  by  equations  (6)  and  (4),  the  (total) 
intensity,  i,  in  a  horizontal  plane  beneath  the  lamp,  at  the 
horizontal  distance  lh  from  the  lamp,  where  lv  is  the  height 
of  the  lamp  above  this  plane  (the  street). 

These  values  of  illumination,  i,  are  plotted,  with  x  =  -  as  ab- 

LV 

scissas,  in  Fig.  101  and  recorded  in  Table  III  for  lv  =  20,  and 
lamps  of  200  mean  spherical  candle  power. 

105.  With  lamps  placed  at  equal   distances  4o,  and  equal 


FIG.  102. 

heights  lv,  as  shown  diagrammatically  in  Fig.  102,  the  illumina- 
tion of  any  point  A  of  the  street  surface  is  due  to  the  light  flux 
of  a  number  of  lamps,  and  not  only  to  the  two  lamps  1  and  2, 
between  which  the  point  A  is  situated.  As,  however,  the  illumi- 
nation rapidly  decreases  with  the  distance  from  the  lamp,  it  is 
sufficient  to  consider  only  the  four  lamps  nearest  to  the  point  A. 
The  illumination  of  a  point  A  of  the  street  surface,  at  a  horizon- 
tal distance  lh  from  a  lamp,  1,  then  is: 

i  =  ^  +  i2  +  ,;  +  ^  (15) 

where  iv  iv  is,  i4  are  the  illumination  due  to  the  lamps  1,  2,  3,  4, 
respectively. 

I  j 

Let  -r  =  P     and     ^==x;  (16) 

k  lv 

then  the  directions  under  which  point  A  receives  light  are  given 
by: 


tan  fa  =  x, 

tan  fa  =  p  —  x, 

tan  fa  =  p  +  x, 

tan  fa  =  2  p  —  x} 


(17) 


LIGHT  INTENSITY  AND  ILLUMINATION. 


239 


and 


1      lv2  cos2 

/ 


V  cos 


cos 


/4 


cos 


(18) 


where  Iv  I2,  73,  I4  are  the  intensities  of  the  light  source  in  the 
respective  directions  <f>v  <f>2, 


100          120  110 

FIGS.  103,  104. 

Herefrom  are  calculated  the  illumination,  i,  plotted  in  Figs.  103 
and  104  and  recorded  in  Table  IV  for  lv  =  20  ft. ;  p  =  5,  hence 
lho  =  100  ft.,  Fig.  103,  and  p  =  10,  hence  lho  =  200  ft.,  Fig.  104, 
for  equal  light  flux  of  200  mean  spherical  candle  power  per  lamp. 

As  seen,  with  the  same  light  flux  per  lamp,  the  distribution 
curve  III  of  Fig.  100  gives  the  highest  and  the  curve  I  the  lowest 
intensity  at  the  minimum  point  midways  between  the  lamps, 
while  inversely  I  gives  the  highest  and  III  the  lowest  intensity 
near  the  lamp;  that  is,  I,  the  carbon  arc  with  clear  inner  globe, 
gives  the  least  uniform,  and  III,  the  luminous  arc,  the  most  uni- 


240 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


form,  illumination,  while  the  carbon  arc  with  opal  inner  globe, 
II,  stands  intermediate. 

TABLE  IV.  —  (Figs.  101  to  106.)      STREET  ILLUMINATION. 


tan  <h  =  x 
tan  02  =  p  —  x 


tan  <J»3  = 
tan  <f>4  = 


X. 

Equal  light  flux  per  lamp. 

Equal  illumination  at  minimum. 

p  =  10. 

p=  5. 

p  =  10. 

p=  5. 

a. 

6. 

c. 

a. 

&. 

c. 

a. 

b. 

c. 

a. 

6. 

c. 

0 
0.2 
0.4 

0.6 
0.8 
1.0 

1.2 
1.4 
1.6 

1.8 
2.0 
2.5 

3.0 
3.5 
4.0 
5.0 

15.8 
22.8 
46.8 

74 
74 
68 

54 
40 
32 

26 
20 
12.7 

8.2 
6.3 
4.9 
4.2 

23.7 
25.7 
34.7 

44 
46 
42 

37 
32 
27 

23 
19.5 
14.6 

11.3 
9 
8 
6.7 

31.7 
32.7 
33.5 

33.5 
33 
32 

30.5 
29 
26.5 

24.5 
22 
18 

15 
13 
11.5 
10.2 

20 
27 
51 

78 
78 
72.5 

59 
45 
37 

32 
29 
25 

29 
31 
40 

50 
52 
48 

43 
38.5 
35 

32.5 
30 

29 

41.5 
42.5 
43 

43 
43 
42.5 

41.5 
40.5 
39 

37.5 
36 
34.5 

38 
54 
111 

176 
176 
162 

128 
95 
76 

62 
48 
30 

20 
15 
12 
10 

35 
38 
52 

66 
69 
63 

55 
48 
40 

34 
29 

22 

17 
13.5 
12 
10 

31 
32 
32.7 

32.7 
32.3 
31.4 

30 

28.4 
26 

24 
22 

18 

15 
13 
11 
10 

8 
11 
20 

31 
31 
29 

24 
18 
15 

13 

11.6 
10 

10 

11 

14 

17 
18 
17 

15 
13 
12 

11 
10.4 
10 

12.  1~2 
12.3 
12.5 

12.5 
12.5 
12.3 

12.1 
11.8 
11.3 

11 
10.5 
10 

Ratio  of  minimum  intensities. 

Ratio  of  total  light  fluxes. 

1 

1.60 

2.43 

1 

1.16 

1.38 

5.95 
2.43 

3.75 
1.53 

2.45 
1.00 

4.0( 
1.3* 

)    3.45    2.90 
1    1.19    1.00 

Ratio  of  maximum  to  min.  ilium. 

17.6 

6.9 

3.3 

3.1 

1.8      1.25 

The  ratio  of  maximum  to  minimum  illumination  is : 

p  =  10  p  =  5 

I.  Carbon  arc  with  clear  globe:                        17.6  3.1 

II.   Carbon  arc  with  opal  globe:                          6.9  1.8 

III.  Luminous,  or  magnetite,  arc :                       3.3  1.25 


LIGHT  INTENSITY  AND  ILLUMINATION. 


241 


As  seen,  lower  values  of  p,  that  is,  either  shorter  distances 
between  the  lamps,  or  greater  elevation  of  the  lamps  above  the 
street  surface,  give  a  more  uniform  illumination,  so  that,  for 
p  =  5,  III  gives  only  25  per  cent  intensity  variation,  while,  for 
p  =  10,  I  gives  a  very  unsatisfactory  illumination,  alternating 
darkness  and  blinding  glare. 


•0=2- 


iO 


100 


140 


160 


r\ 


i 


FIGS.  105,  106. 

In  Figs.  105  and  106  are  plotted,  and  recorded  in  Table  III,  the 
illuminations  for  equal  minimum  intensity  midways  between  the 
lamps,  and  for  equal  distances  lho  =  200  ft.,  between  the  lamps, 
for 

p  =    5,  or  lv  =  40  ft.  height  above  the  street  level,  Fig.  105. 

p  =  10,  or  10  =  20  ft.  height  above  the  street  level,  Fig.  106. 

To  produce  this  minimum  intensity  of  0.1  candle  feet,  with 
200  feet  distance  between  the  lamps,  would  require  the  following 
mean  spherical  candle  powers  : 


I.   Carbon  arc  with  clear  globe:     1190 

II.  Carbon  arc  with  opal  globe:       750 

III.   Magnetite  arc:  490 


,  or  4=40  ft. 
800 
690 
580 


242  RADIATION,  LIGHT,  AND  ILLUMINATION. 

It  is  interesting  to  note  the  great  difference  in  the  light  flux, 
required  to  produce  the  same  minimum  illumination,  for  the 
three  distribution  curves. 

The  carbon  arc  gains  in  efficiency  and  in  uniformity  of  illumi- 
nation by  increasing  the  elevation  from  20  to  40  ft.,  while  the 
magnetite  arc  loses  in  efficiency  —due  to  the  greater  distance 
from  the  illuminated  surfaces  —but  makes  up  for  this  by  the 
gain  in  uniformity  of  illumination. 


C.   ROOM  ILLUMINATION  BY  INCANDESCENT 

LAMPS. 

106.  Let  Fig.  107  represent  the  intensity  distribution  of  an 
incandescent  lamp  with  reflector,  suitably  designed  for  approxi- 
mately uniform  illumination  in  a  horizontal  plane  below  the 
lamp.  Such  a  distribution  curve  can,  for  instance,  be  produced 


FIG.  107. 

by  a  spiral  filament  F  (Fig.  108)  located  eccentric  in  a  spher- 
ical globe  G,  of  which  the  upper  part  is  clear  glass  and  covered 
by  a  closely  attached  mirror  reflector  R,  while  the  lower  part 
is  frosted,  as  shown  diagrammatically  in  Fig.  105. 

With  this  arrangement,  half  of  the  light  flux  issues  directly, 
with  approximately  uniform  intensity  in  the  lower  hemisphere, 
from  <j>  =  0  to  <j>  =  (f>l}  and  with  gradually  decreasing  intensity 
from  $  =  <£j  to  0  at  <£  =  <j>2.  The  other  half  of  the  light  flux  is 


LIGHT  INTENSITY  AND  ILLUMINATION. 


248 


reflected  from  the  mirror,  and,  due  to  the  eccentric  location  of  the 
filament,  the  reflected  rays  are  collected  into  an  angle  of  about 
45  deg.  from  the  vertical,  and  cross  each  other,  thereby  producing 
the  intensity  maximum 
at  4>  =  30  deg.  The 
intrinsic  brilliancy  is 
sufficiently  reduced, 
and  the  distribution 
curve  smoothed  out, 
by  the  frosting  of  the 
globe  as  far  as  not  cov- 
ered by  the  reflector. 
The  light  in  the  upper 
hemisphere  beyond 
</>  =  (j>2  then  is  only 
that  reflected  by  the 
frosting. 

The  numerical  val- 
ues of  intensity  of  Fig. 
107  are  recorded  in 
Table  V. 

The  mean  spherical 
candle  power  of  the 
lamp  is  12.93,  or  163 
lumens ;  the  mean  can- 
dle power  in  the  lower 
hemisphere  is  20.20,  or 
127  lumens,  and  the  mean  candle  power  in  the  upper  hemi- 
sphere is  5.66,  or  36  lumens. 

Table  V  gives  the  distribution  of  illumination  i  in  a  horizontal 
plane  beneath  and  above  the  lamp,  for  different  horizontal 
distances  lh  and  the  vertical  distance  lv  =  1,  by  equation  (6), 
and  the  horizontal  illumination  ih,  by  equation  (7),  as  discussed 
in  A.  These  are  plotted  in  Fig.  109,  for  the  lower  hemisphere 
in  the  lower,  for  the  upper  hemisphere  in  the  upper,  curve. 

Assuming  now  that  a  room  of  24  ft.  by  24  ft.  and  10  ft.  high 
is  to  be  illuminated  by  four  such  lamps,  located  6  inches  below 
the  ceiling  in  such  a  manner  as  to  give  as  nearly  as  possible 
uniform  illumination  in  a  plane  2.5  ft.  above  the  floor  (the  height 
of  table,  etc.). 


FIG.  108. 


244          RADIATION,  LIGHT,  AND  ILLUMINATION. 


TABLE  V.  —  (Figs.  107  to  109.) 


#. 

7. 

lh 

lv 
tan  c£. 

i  = 

I 

COS2<£ 

**~ 

/ 

Ik 

X  =  TV 

i  — 
I 
cosV 

fc*- 

/ 

cos3^ 

(Upper 
hemisphere). 

cos3  tf, 

if. 

i'h- 

0 
10 
20 

30 
40 
50 

60 
65 
70 

75 
80 

85 

90 
95 
100 

105 
110 
115 

120 
130 
140 

150 
160 
170 

180 

21.0 
22.2 
24.5 

26.3 
25.5 
22.5 

20.0 
19.0 
18.0 

17.0 
16.0 
15.0 

13.0 
11.0 
9.5 

8.0 
7.0 
5.5 

4.5 
3.0 
2.5 

2.2 
2.0 
2.0 

2.0 

0 

0.176 
0.364 

0.577 
0.839 
1.192 

1.732 
2.144 
2.745 

3.732 
5.671 
11.43 

00 

11.43 
5.671 

3.732 
2.745 
2.144 

1.732 
1.192 
0.839 

0.577 
0.364 
0.176 

0 

21.0 
21.5 
21.7 

19.8 
15.0 
9.3 

5.0 
3.4 
2.15 

1.13 
0.49 
0.11 

0 
0.08 
0.29 

0.53 
0.84 
1.00 

1.12 
1.23 
1.47 

1.66 
1.77 
1.94 

2.0 

21.0 
21.3 
20.4 

17.0 
11.5 
6.0 

2.5 
1.44 
0.74 

0.29 
0.08 
0.01 

0 
0.01 

0.08 

0.14 
0.29 
0.42 

0.56 
0.80 
1.13 

1.43 
1.66 
1.91 

2.0 

o 

0.1 
0.2 

0.3 
0.4 
0.5 

0.6 
0.7 
0.8 

0.9 
1.0 
1.1 

1.2 
1.3 
1.4 

1.5 
1.6 
1.7 

1.8 
1.9 
2.0 

2.5 
3.0 
3.5 

4.0 
4.5 
5.0 

6.0 
7.0 
8.0 

9.0 
10.0 

21.0 

21.25 
21.55 

21.8 
21.6 
20.8 

19.4 
17.7 
15.8 

13.9 
12.2 
10.6 

9.2 
5.1 
7.2 

6.45 
5.8 
5.2 

4.7 
4.2 
3.9 

2.55 
1.8 
1.33 

1.0 
0.8 
0.67 

0.45 
0.33 
0.25 

0.20 
0.17 

21.0 
21.1 
21.3 

21.0 
20.0 
18.5 

16.5 
14.3 
12.3 

10.4 
8.6 
7.2 

6.0 
5.1 

4.2 

3.55 
3.1 
2.65 

2.25 
1.95 
1.7 

1.0 
0.6 
0.37 

0.25 
0.18 
0.13 

0.10 
0.08 
0.05 

2.0 

2.0 

*i'.i 

1.5 

1.35 

1.0 

1.2 

0.68 

Y.08 

0.9 
0.77 
0.63 

0.5 
0.43 
0.38 

0.28 
0.20 
0.17 

0.14 
0.12 

'b'.48 

0.35 
0.27 
0.20 

0.13 
0.10 
0.08 

0.06 

As  the  illumination  in  the  space  between  the  lamps  is  due 
to  several  lamps  and  thus  is  higher  than  that  at  the  same  horizon- 
tal distance  outside  of  a  lamp,  for  approximate  uniformity 
of  illumination,  the  distance  between  the  lamps  must  be  con- 
siderably greater  than  twice  their  distance  from  the  side  walls 


LIGHT  INTENSITY  AND  ILLUMINATION.  245 


0*6 


08 


II 


246 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


of  the  room.  Locating  thus  the  lamps,  as  shown  diagrammati- 
cally  in  Fig.  110,  at  5  ft.  from  the  side  walls  and  14  ft.  from  each 
other,  the  (total)  illumination  in  the  lines  A,  B,  C,  D  in  the 
test  plane  2.5  ft.  above  the  floor  is  calculated.  As  this  plane  is 
7  ft.  beneath  the  lamps,  first  the  illumination  curve  in  a  plane 
7  ft.  beneath  the  lamp  is  derived  from  that  in  Fig.  109,  by 
dividing  the  ordinates  by  72  =  49,  and  multiplying  the  abscissas 
by  7.  It  is  given  in  Fig.  111. 


FIG.  111. 

The  illumination,  i,  at  any  point,  P,  then  is  derived  by  adding 
the  illumination  ia,  ib,  ic,  id  of  the  four  lamps  a,  6,  c,  d,  taken 
from  curve  in  Fig.  Ill  for  the  horizontal  distances  of  point  P 
from  the  lamps :  lhg,  lhb,  lhc,  lhd.  These  component  illuminations 
are  plotted  in  Figs.  112  to  115;  as  A  ,  Ab,  Ac,  Ad  in  Fig.  112;  as 
Ba,  Bb  in  Fig.  113,  etc.,  and  their  numerical  values,  in  thousandths 
of  candle  feet,  recorded  in  Table  VI.  In  Fig.  116  are  shown 
the  four  curves  of  the  resultant  direct  illumination,  superim- 
posed upon  each  other. 

107.  To  this  direct  illumination  is  to  be  added  the  diffused 
illumination  G  resulting  from  reflection  by  ceiling  and  walls. 

Let:  at  =  0.75  =  albedo  of  ceiling; 

a2  =  0.4    =  albedo  of  walls; 


(19) 


while  the  floor  may  be  assumed  as  giving  no  appreciable  reflec- 
tion: a  =  0.  The  diffused  light,  then,  may  be  approximated 
as  follows: 

The  ceiling  receives  as  direct  light  the  light  issuing  in  the  upper 
hemisphere,  or  36  lumens  per  lamp,  thus  a  total  of 

Lx  =  4  X  36  =  144  lumens,  (20) 


LIGHT  INTENSITY  AND  ILLUMINATION. 
TABLE  VI.  —  (Figs.  110  to  116.) 


247 


X. 

Aa. 

Ab. 

A. 

Ba 
and 
Bd- 

B. 

ca. 

cb. 

C. 

Da- 

Db 
and 
Dc. 

D. 

0 

353 

71 

746 

180 

690 

244 

43 

600 

245 

43 

600 

1 

406 

74 

813 

200 

738 

276 

44 

645 

317 

49 

691 

2 

438 

76 

852 

218 

782 

306 

44 

681 

395 

55 

785 

3 

442 

78 

866 

234 

822 

332 

45 

714 

441 

62 

845 

4 

438 

80 

875 

244 

852 

348 

45 

737 

440 

70 

866 

5 

429 

80 

880 

247 

870 

353 

45 

746 

429 

79 

880 

6 

438 

80 

903 

244 

882 

348 

45 

754 

440 

90 

919 

7 

442 

78 

922 

234 

880 

332 

45 

750 

441 

101 

949 

8 

438 

76 

936 

218 

866 

306 

44 

737 

395 

114 

939 

9 

406 

74 

927 

200 

850 

276 

44 

723 

317 

125 

896 

10 

353 

71 

898 

180 

838 

244 

43 

710 

245 

135 

859 

11 

298 

67 

875 

162 

830 

209 

42 

696 

184 

143 

835 

12 

247 

63 

870 

144 

825 

180 

41 

690 

144 

144 

825 

13 

flOO 

60 

129 

156 

39 

115 

143 

14 

167 

57 

114 

136 

37 

94 

135 

15 

143 

54 

102 

118 

35 

79 

125 

16 

121 

51 

90 

103 

33 

66 

114 

17 

104 

48 

81 

90 

31 

56 

101 

18 

90 

45 

72 

80 

30 

49 

90 

19 

80 

41 

63 

72 

30 

42 

79 

20 

70 

38 

57 

64 

30 

36 

70 

21 

61 

35 

52 

58 

29 

33 

62 

22 

55 

33 

48 

52 

29 

30 

55 

23 

52 

31 

44 

47 

28 

26 

49 

24 

45 

2P 

40 

43 

28 

23 

43 

and  also  receives  some  reflected  light  from  the  walls.  Thus, 
if  ^  =  total  light  flux  received  by  the  ceiling,  and  3>2  =  total 
light  flux  received  by  the  walls,  the  light  flux  received  by  the 
ceiling  is 

^  =  L,  +  b2a23>2,  (21) 

where  b2  is  that  fraction  of  the  light  flux  issuing  from  the  walls, 
which  is  received  by  the  ceiling. 
And  the  light  reflected  from  the  ceiling  thus  is : 

$/=  afr  =  a,  (L,  +  b2a2$>2).  (22) 

The  walls  receive  as  direct  light  the  light  issuing  from  the 
lamps  in  the  lower  hemisphere,  between  the  horizontal,  <f>  =  90 


248 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


deg.,  and  the  direction,  <£  =  a)  (Fig.  110),  from  the  lamp  to  the 
lower  edge  of  the  walls.  This  angle  co  varies,  and  averages 
30  deg.  for  that  half  of  the  circumference,  PQR  (Fig.  110),  at 
which  the  walls  are  nearest,  and  60  deg.  for  that  half,  RSTUP, 
for  which  the  walls  are  farthest,  from  the  lamp.  Hence  the 


1.0 


0.8 


0.6 


0.4 


0.2 


Act 


Ac 


12  10 


0.8 

B 
0.6 

0.4 

G 
0,2 

BaScd 

BbStc 

6       *c 

B 

B 

G 

Bfc&c 

Bakd 

X 

x-  — 

**  -^ 

-^ 

-* 

^» 

-•>s 

X 

/ 

\ 

-*- 

^^ 

^^** 

>J 

^ 

_        ~~ 

_   - 

—.  •— 

,  —  • 

-  — 

-     -, 

~-  .. 

••      — 

4                  8                 12                18                20               2* 

FIGS.  112,  113. 

light  flux  received  by  the  walls  as  directed  light,  from  each  lamp, 
is 

-  I     I  sin  $  d$  +  -  T    /  sin  $  d$  =  83  lumens;         (23) 

Zt/30°  ^^60° 

or,  a  total  of  L2  =  4  X  83  =  332  lumens.  (24) 


LIGHT  INTENSITY  AND  ILLUMINATION. 


249 


In  addition  hereto,  the  walls  receive  some  of  the  light  flux 
reflected  by  the  ceiling.  The  total  light  received  by  the  walls 
thus  is : 

$2  =  L2  +  bpfr,  (25) 

where  bl  is  that  fraction  of  the  light  flux  issuing  from  the  ceiling, 
which  is  received  by  the  walls. 


1.0 


0.8 


0.6      C 


G 

0.2    Ca 


Cb 

Cd 

0     Cc 


1.0 


Cb 


12  16  20 


0.8 


0.8      D 


O.i 


0.2 


Dbbd 
0       DC 


Da 


FIGS.  114,  115. 
And  the  light  reflected  from  the  walls  thus  is : 

*,'  -  a^2  =  a2  (L2  +  6^*,).  (26) 

It  thus  remains  to  calculate  the  numerical  values  of  bl  and  by 
Of  the  light  reflected  by  the  ceiling  as  secondary  generator, 
/,  a  part  is  obstructed  by  the  floor,  a  part  received  by  the  walls. 


250 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


The  floor  is  a  square  plane,  of  the  same  size,  24  by  24  ft.,  as  the 
radiator,  that  is,  the  ceiling,  and  at  the  distance  10.  The  light 
intercepted  by  the  floor  can  thus  approximately  be  calculated 
as  discussed  in  Lecture  X,  II,  1,  Fig.  82,  for  circular  radiator 
and  circular  shades,  by  replacing  the  quadratic  shade  and  radia- 
tor by  circular  shades  of  the  same  area,  r2n  =  242,  and  r  = 

13.5,  at  the  same  distance  I  =  10,  hence  of  the  ratio :  -  =  0.74. 

Calculated  as  discussed  in  Lecture  X,  II,  1,  the  floor  receives 
55  per  cent  and  the  walls  45  per  cent  of  the  light  reflected  by  the 
ceiling. 

Assuming,  approximately,  that  the  walls  receive  the  same 
percentage  of  the  light  reflected  from  the  ceiling,  as  the  ceiling 
receives  of  the  light  reflected  from  the  walls,  or 

&2  -  &!,  (27) 
equations  (21)  and  (25)  become: 

^  =  L,+  \a2$>2,  (28) 

<f>2  =  L2+  6^^;  (29) 


hence, 


_L2+ 

2  1    + 


(30) 


and  the  light  reflected  from  the  ceiling  is 

$/  =  a^  =  «A  — —  *  2  2; 
the  light  reflected  from  the  walls  is 

<L  '  dS  ^2~^~  biaiLl 


(30) 


hence,  substituting  the  numerical  values  : 

$/  =  146  lumens  and  $/  =  144  lumens  " 

are  the  values  of  light  reflected  from  the  ceiling  and  from  the 
walls  respectively. 

Of  that  from  the  ceiling,  the  floor  receives  (1  -  6J  =  0.55, 
and  of  that  from  the  walls,  the  floor  receives  ll  =  0.45;  hence, 


LIGHT  INTENSITY  AND  ILLUMINATION. 


251 


the  diffused  light  on  the  floor  plane,  and  thus  also,  sufficiently 
approximate,  on  the  test  plane  2.5  ft.  above  the  floor,  is 

*.=  (!  -&,)*,'+&,*,' 

=  145  lumens, 

and  as  this  plane  contains  At  =  576  sq.  ft.,  the  flux  of  diffused 
light  per  square  foot  in  the  test  plane,  or  the  diffuse  illumination, 

is  L  =  -r  =  0.250  foot-candle. 


r.oo 


500 


400 


300 


200 


100 


/ 
£ 

/ 


FIG.  116. 

108.  Adding  this  diffuse  illumination,  shown  as  G,  to  the 
directed  illumination,  gives  the  total  illumination,  i,  shown 
as  A,  B,  C,  Dm  Figs.  112  to  115,  and  recorded  in  Table  VI. 

From  these  curves  are  taken  the  values  of  the  distance, 
Table  VII,  at  which  the  total  illumination  passes  0.600;  0.650; 
0.700,  etc.,  foot-candle,  and  plotted  in  Fig.  117.  The  points  of 
equal  illumination,  then,  are  connected  by  curves,  and  thus 
give  what  may  be  called  equi-luminous  curves,  or  equi-potential 
curves  of  illumination. 

These  equi-luminous  curves  are  plotted  for  every  0.05  foot- 
candle,  except  that  the  curves  0.875  and  0.925  are  added  in 


252          RADIATION,  LIGHT,  AND  ILLUMINATION. 

dotted  lines.  As  seen,  the  illumination  is  a  minimum  of  0.600 
in  the  corners  of  the  room  and  a  maximum  of  0.950  at  a  point 
between  the  lamps  and  the  center  of  the  room,  and  is  between 
0.800  and  0.950  everywhere  except  close  to  the  edges  of  the 
room. 


FIG.  117 


TABLE  VII.— (Fig.  117.)    EQUI-POTENTIAL  CURVES. 


t. 

A. 

B. 

C. 

D. 

600 

o 

o 

625 

55 

28 

650 

1  15  rC440)l 

56 

675 

1  80  L12  OOJ 

82 

700 

.20 

2  57   10  70 

1  09 

725 

70 

3  45    8  85 

1  37 

750 
775 
800 
825 

.05 
.37 

.77 
1.21  f  (620)1 

1.24 
1.88 
2.45  r(576)l 
3.08  Ll2  OOJ 

5.50    7.00 
6.30 

(505) 

1.61 
1.88 
2.18  r(576)l 
2  50  L12.00J 

850 

1.90  Ll2.00J 

3.88    9.00 

3  10   10.35 

875 

4.00   11.00 

5.30    7.47 

4  70    9.50 

900 

5.90    9.90 

6.40 

5.53    8.90 

925 

7.15    9.10 

(634) 

6.13    8.32 

950 

8.20 

7  20 

(686^ 

Cjc\f\\ 

LIGHT  INTENSITY  AND  ILLUMINATION.  253 

The  direct  light,  which  reaches  the  test  plane,  2.5  ft.  above 
the  floor,  as  directed  light  from  the  lamps,  issues  within  the  angle 
from  the  vertical,  <£  =  0,  up  to  from  <£  =  40  deg.  to  0  =  70 
deg.,  and  is  75  lumens  per  lamp;  or,  a  total  of  directed  light  in 
the  test  plane  of  4  X  75  =  300  lumens.  The  diffused  light  in 
the  test  plane  is  576  X  0.25  =  144  lumens,  and  the  total  light 
in  the  test  plane  thus  is  444  lumens;  while  the  total  light 
issuing  from  the  four  lamps  is  4  X  163  =  652  lumens,  giving  an 

444 

efficiency  of  illumination  of  ;  -  =  0.68;   or,  68  per  cent:   the 

652 

444 

average  horizontal  illumination  in  the  test  plane  is  ihm  =  — -  = 

o7o 

770;  while  the  average  total  illumination,  from  Fig.  117,  is 
about  im  =  870.  The  difference  is  due  to  the  varying  direction 
in  which  the  directed  light  traverses  the  test  plane. 

Measurement  of  the  illumination  of  a  room  by  illuminometer, 
to  give  correct  values,  thus  must  take  in  consideration  the 
different  directions  in  which  the  light  traverses  every  point; 
by  measuring  the  light  flux  intercepted  by  a  horizontal  sur- 
face, the  result  represents  only  the  horizontal  illumination, 
and  not  the  total  illumination  at  the  point  measured,  and 
therefore  frequently  does  not  represent  the  illuminating  value 
of  the  light. 

D.  HORIZONTAL  TABLE  ILLUMINATION  BY  INCAN- 
DESCENT LAMPS. 

109.  Assuming  a  table,  of  5  ft.  by  13  ft.,  to  be  illuminated 
so  as  to  give  as  nearly  as  possible  uniform  horizontal  illumina- 
tion ih.  With  a  light  source  of  the  distribution  curve,  Fig.  107, 
but  of  four  times  the  intensity,  and  using  two  such  lamps,  they 
would  be  located  vertically  above  the  table,  at  a  distance  from 
each  other  which  would  be  chosen  so  that,  midways  between 
the  lamps,  the  illumination  is  approximately  the  same  as  verti- 
cally beneath  the  lamps. 

In  the  same  manner  as  discussed  in  C,  the  illumination  is 
calculated  in  characteristic  lines,  indicated  as  A,  B,  C  in  Fig. 
118,  using,  however,  the  curve  ih  of  Fig.  109. 

About  the  most  uniform  horizontal  illumination  then  is  given 
by  locating  the  lamps  5  ft.  above  the  table,  8  ft.  from  each 


254          RADIATION,  LIGHT,  AND  ILLUMINATION. 

other  and  2.5  ft.  from  the  edge  of  the  table,  as  shown  in  Fig.  118. 
The  illuminations  in  the  lines  A,  B,  and  C,  and  their  components 
are  plotted  in  Figs.  119,  120,  121,  and  recorded  in  Table  VII. 


A — 


1 

( 

f  '             T 

(f 

k---J 

B.  ^ 

fr-2.5—  » 

, 

^  4  ^ 

v       _ 

2J5 

"^ 

2|5 
i 

6 

FIG.  118. 


TABLE  VIII.—  (Figs.  118  to  121.)    HORIZONTAL  ILLUMI- 
NATION OF  TABLE. 


X. 

Aa. 

Ab. 

A. 

Ba. 

Bb. 

B. 

Ca'b. 

C. 

-2.5 
-2.0 
—  1.5 

2.96 
3.20 
3.36 

0.24 
0.27 
0.32 

3.20 
3.47 
3.68 

2.96 
3.20 
3.36 

0.38 
0.46 
0.48 

3.34 

3.66 
3.84 

1.55 
1.66 
1.79 

3.10 
3.32 
3.58 

—  1.0 
—  0.5 
0 

3.41 
3.37 
3.36 

0.37 
0.43 
0.50 

3.78 
3.80 
3.86 

3.41 
3.37 
3.36 

0.48 
0.50 
0.50 

3.89 
3.87 
3.86 

1.89 
1.96 
1.97 

3.78 
3.92 
3.94 

+  0.5 
1.0 
1.5 

3.37 
3.41 
3.36 

0.57 
0.67 
0.81 

3.94 
4.08 
4.17 

3.37 
3.41 
3.36 

0.50 
0.48 
0.48 

3.87 
3.89 
3.84 

1.96 
1.89 
1.79 

3.92 
3.78 
3.58 

2.0 
2.5 
3.0 

3.2 
2.96 
2.63 

0.96 
1.15 
1.37 

4.16 
4.11 
4.00 

3.20 
2.96 

0.46 
0.38 

3.66 
3.34 

1.66 
1.55 

3.32 
3.10 

3.5 

2.28 

1.66 

3  94 

+  4.0 

1.96 

1.96 

3.92 

LIGHT  INTENSITY  AND  ILLUMINATION. 


255 


From  the  curves  as  given  in  Figs.  119  to  121  may  then  be 
plotted  the  equi-luminous  curves  at  the  table  surface,  as  done 
in  Fig.  117  of  the  preceding  paragraph.  In  this  case,  which 
represents  concentrated  illumination,  diffusion  is  not  considered, 
but  the  light  is  all  directed  light. 


A 


141 

FIG.  119. 


4.0 


3.0 


2.0 


1.0 


4,0  4.0 


3.0  3.0 


2.0  2.0 


1.0 


/" 

N, 

/ 

\ 

^ 

^ 

"""-- 

\ 

i 

FIG.  120. 


FIG.  121. 


LECTURE  XII. 
ILLUMINATION  AND   ILLUMINATING  ENGINEERING. 

110.  Artificial  light  is  used  for  the  purpose  of  seeing  and 
distinguishing  objects  clearly  and  comfortably  when  the  day- 
light fails.  The  problem  of  artificial  lighting  thus  comprises  con- 
sideration of  the  source  of  light  or  the  illuminant;  the  flux  of 
light  issuing  from  it;  the  distribution  of  the  light  flux  in  space, 
that  is,  the  light  flux  density  in  space  and  more  particularly  at 
the  illuminated  objects;  the  illumination,  that  is,  the  light  flux 
density  reflected  from  the  illuminated  objects,  and  the  effect 
produced  thereby  on  the  human  eye.  In  the  latter,  we  have  left 
the  field  of  physics  and  entered  the  realm  of  physiology,  which  is 
not  as  amenable  to  exact  experimental  determination,  and  where 
our  knowledge  thus  is  far  more  limited  than  in  physical  science. 
This  then  constitutes  one  of  the  main  difficulties  of  the  art  of 
illuminating  engineering:  that  it  embraces  the  field  of  two  dif- 
ferent sciences  —  physics  and  physiology. 

The  light  flux  entering  the  eye  is  varied  in  its  physical  quantity 
by  the  reaction  of  the  eye  on  light  flux  density  in  contracting 
or  expanding  the  pupil.  The  effect  of  the  light  flux  which  enters 
the  eye  is  varied  by  the  fatigue,  which  depends  on  intensity  and 
also  on  color.  Distinction  is  due  to  differences  in  the  light  flux 
density  from  the  illuminated  objects,  that  is,  differences  of 
illumination,  which  may  be  differences  in  quality,  that  is,  in 
color,  or  differences  in  intensity,  that  is,  in  brightness,  and  as 
such  includes  the  effect  of  shadows  as  causing  differences  in 
intensity  at  the  edge  of  objects. 

The  physical  quantities  with  which  we  have  to  deal  in  illumi- 
nating engineering  thus  are : 

The  intensity  of  the  light  source  or  the  illuminant,  and  its 
brilliancy,  that  is,  the  flux  density  at  the  surface  of  the 
illuminant; 

The  flux  of  light,  that  is,  the  total  visible  radiation  issuing 
from  the  illuminant; 

256 


ILLUMINATION  AND  ILLUMINATING  ENGINEERING.     257 

The  light  flux  density,  that  is,  the  distribution  of  the  light  flux 
in  space,  and 

The  illumination,  that  is,  the  light  flux  density  issuing  from 
the  illuminated  objects. 

The  intensity  of  a  light  source  is  measured  in  candles.  The  unit 
of  light  intensity,  or  the  candle,  is  a  quantity  not  directly  related 
to  the  absolute  system  of  units,  but  reproduced  from  specifica- 
tions or  by  comparison  with  maintained  standards,  and  for 
white  light  is  probably  between  0.04  and  0.02  watt.  Intensity 
has  a  meaning  only  for  a  point  source  of  light;  that  is,  an  illumi- 
nant  in  which  the  flux  of  light  issues  from  a  point  or  such  a  small 
area  that,  at  the  distance  considered,  it  can  be  considered  as  a 
point.  "  Intensity  of  light "  thus  is  a  physical  quantity  of  the 
same  nature  as  " intensity  of  magnet  pole,"  which  latter  also 
presupposes  that  the  total  magnetic  flux  issues  from  a  point, 
and  thus  is  applicable  only  when  dealing  with  such  distances 
from  the  source  of  the  light  flux  or  magnetic  flux,  that  the  flux 
can  be  assumed  as  issuing  from  a  point.  Frequently  the  inten- 
sity of  a  light  source  is  different  in  different  directions,  and  then 
either  the  distribution  curve  of  the  light  intensity  is  required  for 
characterizing  the  illuminant,  or  the  average  of  the  intensities  in 
all  directions  in  space  is  used,  and  is  called  the  "mean  spherical 
intensity." 

The  unit  of  light  intensity,  or  the  candle,  is  the  intensity 
which  produces  unit  flux  density  at  unit  distance  from  the  light 
source,  and  thus  produces  a  total  flux  of  light  equal  to  4  n 
units  (the  surface  of  the  sphere  at  unit  distance  from  the  light 
source).  The  unit  of  light  flux  is  called  the  lumen,  and  one 
candle  of  light  intensity  thus  produces  4  n  lumens  of  light  flux 
(just  as  a  magnet  pole  of  unit  intensity  produces  4  x  lines  of 
magnetic  force). 

The  light  flux  is  the  essential  quantity  which  characterizes 
the  usefulness  of  an  illuminant,  and  it  is  the  raw  material  from 
which  all  illuminating  engineering  starts.  Any  source  of  light 
can  be  measured  in  units  of  light  flux  or  lumens  —  the  diffused 
daylight  entering  the  windows  of  a  room,  or  the  visible  radia- 
tion of  the  mercury  lamp  or  a  Moore  tube  as  well  as  that  of  a 
point  source  —  by  adding  all  the  flux  densities  intercepted  by 
any  surface  enclosing  the  source  of  light. 

In  a  point  source  of  light,  the  intensity,  in  candles,  is  the  total 


258  RADIATION,  LIGHT,  AND  ILLUMINATION. 

flux  of  light,  in  lumens,  divided  by  4  x.  In  any  illuminant 
which  is  not  a  point  source,  we  cannot  speak  of  an  intensity, 
except  at  such  distances  at  which  the  source  of  light  can  be 
assumed  as  a  point;  and  in  interior  illumination  this  is  rarely 
the  case.  Since,  however,  the  candle  power,  as  measure  of  the 
intensity  of  light,  has  become  the  most  familiar  quantity  in 
characterizing  illuminants,  very  commonly  even  sources  of  light 
which  are  not  point  sources  —  as  a  Moore  tube  or  the  diffused 
daylight  — are  expressed  in  " equivalent  candle  power"  and  when 
thus  speaking  of  the  candle  power  of  a  mercury  lamp,  or  of  the 
diffused  daylight  from  the  windows,  we  mean  the  candle  power 
of  a  point  source  of  light,  which  would  give  the  same  total  flux 
of  light  as  the  mercury  lamp,  or  the  daylight  from  the  windows, 
etc.  The  "  equivalent  candle  power,"  or  frequently  merely  called 
"  mean  spherical  candle  power/'  thus  is  the  total  light  flux  divided 
by  4  TT,  hence  in  reality  is  not  a  unit  of  intensity,  but  a  unit  of 
light  flux. 

This  explains  the  apparent  contradiction  between  the  claims 
that  sources  of  light,  as  the  mercury  lamp  or  the  Moore  tube,  can- 
not be  expressed  in  candle  powers,  while  at  the  same  time  their 
specific  consumptions  are  given  in  candle  power  per  watt :  mean- 
ing equivalent  candle  power,  which  refers  to  the  total  flux  of 
light,  and  thus  is  a  definite  and  measurable  physical  quantity. 

While  it  is  not  probable  that  the  custom  of  rating  illuminants 
in  candles,  regardless  of  their  shape,  will  quickly  disappear,  and 
no  objection  exists  against  it,  provided  that  it  is  understood  to 
mean  the  equivalent  candle  power,  it  is  preferable  to  use  the  cor- 
rect unit  of  light  flux,  and  express  the  output  of  a  source  of  light 
in  lumens,  adding  where  necessary  the  equivalent  candle  power 
in  parenthesis.  Obviously,  the  use  of  the  candle  power  in  any 
particular  direction  —  horizontal,  or  terminal,  or  maximum  can- 
dle power — has  a  meaning  only  in  characterizing  the  distribution 
of  the  light  flux,  as  applicable  for  a  particular  purpose,  as  street 
lighting,  but,  when  used  for  rating  the  illuminant  by  its  light  flux 
output,  is  an  intentional  or  unintentional  deception.  Incandes- 
cent lamps  have  been  rated,  and  to  some  extent  still  are,  in  hori- 
zontal candle  power,  but  in  this  case  the  horizontal  candle  power 
has  ceased  to  mean  the  actual  horizontal  candle  power,  but  is 
the  horizontal  candle  power  which  with  a  certain  standard  dis- 
tribution of  light  flux  would  correspond  to  the  light  flux  of  the 


ILLUMINATION  AND  ILLUMINATING  ENGINEERING.     259 

lamp,  and  thus  also  is  merely  a  practical  measure  of  the  light 
flux,  retained  by  convenience :  one  horizontal  candle  power  rep- 
resents 0.78  mean  spherical  or  equivalent  candle  power  of  the 
standard  distribution  curve,  and  thus  4  TT  X  0.78  lumen. 

In  general,  intensity,  or  candle  power,  thus  is  an  angular 
measure,  useful  in  characterizing  the  distribution  of  the  light 
flux,  but  not  the  total  light  flux. 

111.  Light- flux  density  is  the  light  flux  per  unit  area  traversed 
by  it,  thus  is  measured  in  lumens  per  square  meter  (or  square 
foot),  just  as  the  magnetic  density  is  measured  in  lines  of  mag- 
netic force  per  square  centimeter.  In  illumination,  as  unit  of 
length,  usually  the  meter  is  employed,  and  not  the  centimeter,  as 
in  the  absolute  system  of  units,  and  102  thus  is  the  reduction 
factor  to  absolute  units.  Frequently  also  the  foot  is  used  as 
practical  unit  of  length. 

For  a  point  source  of  light  the  light  flux  density  is  the  inten- 
sity of  the  light  source,  in  candles  (in  the  direction  towards  the 
point  of  observation,  if  the  distribution  is  not  uniform  in  all 
directions),  divided  by  the  square  of  the  distance,  in  meters, 
or  feet,  and  the  light  flux  density  thus  is  frequently  expressed 
in  meter-candles,  or  foot-candles.  Thus  at  10  feet  distance  from 
a  16  candle  power  lamp,  the  light  flux  density  is  0.16  foot-candle, 
or  0.16  lumen  per  square  foot.  Very  commonly,  therefore, 
the  light  flux  density  produced  by  sources  of  light  which  are 
not  points,  is  also  expressed  in  meter-candles  or  foot-candles — 
which  numerically  is  the  same  value,  that  is,  the  same  quantity, 
as  lumens  per  square  meter  or  square  foot,  but  physically 
would  refer  to  the  equivalent  candle  power  of  the  light  source. 

Illumination  is  the  light  flux  density  reflected  from  the  illu- 
minated object,  and  as  flux  density  thus  is  measured  also  in 
lumens  per  square  meter  or  square  foot,  or  in  meter-candles  or 
foot-candles. 

Brilliancy  is  the  light  flux  density  at  the  surface  of  the  illumi- 
nant,  and  as  flux  density  thus  could  also  be  measured  in  lumens 
per  square  meter  or  square  foot,  but,  as  this  would  usually  give 
enormous  values,  brilliancy  of  the  light  source  generally  is  meas- 
ured in  lumens  per  square  centimeter,  or  per  square  millimeter. 
It  is  a  quantity  which  is  of  high  importance  mainly  in  its  physio- 
logical effect. 

Light  intensity,  brilliancy  and  light  flux  thus  are  character- 


260  RADIATION,  LIGHT,  AND  ILLUMINATION. 

istics  of  the  illuminant,  while  flux  density  is  a  function  of  the 
space  traversed  by  the  light  flux,  but  not  of  the  source  of  light  : 
with  the  same  source  of  light,  in  the  space  from  the  surface  of 
the  illuminant  to  infinite  distance,  all  light  flux  densities  exist 
between  the  maximum  at  the  surface  of  the  illuminant  (its 
brilliancy)  and  zero.  Brilliancy  thus  is  the  maximum  of  the 
light-flux  density.  While  intensity  and  brilliancy  depend  upon 
the  shape  of  the  illuminant,  light  flux  is  independent  thereof. 
Illumination  is  a  quantity  which  depends  not  only  on  the  source 
of  light,  that  is,  light  flux  and  flux  density,  but  also  on  the  illumi- 
nated objects  and  their  nature,  and  thus  is  the  light  flux  density 
as  modified  by  the  illuminated  objects.  Very  commonly,  how- 
ever, the  term  "  illumination "  is  used  to  denote  "  light  flux 
density,"  irrespective  of  the  illuminated  objects. 

112.  The  light  flux  thus  is  the  raw  material  with  which 
illuminating  engineering  starts,  and  the  first  problem  then  is 
to  distribute  the  light  flux  through  space  so  as  to  give  at  all 
points  the  light  flux  density  required  for  satisfactory  illumi- 
nation. 

Some  problems,  as  the  lighting  of  a  meeting  place,  school- 
room, etc.,  require  a  uniform  or  general,  and  fairly  high  intensity 
of  illumination,  while  in  street  lighting  a  uniform  but  fairly  low 
intensity  of  illumination  is  desirable.  In  other  cases,  mainly  a 
local  or  concentrated  illumination  is  needed.  Usually,  however, 
a  combination  of  a  local  or  concentrated  illumination,  of  fairly 
high  intensity,  with  a  general  illumination  of  lower  intensity, 
is  required:  the  former  at  those  places  where  we  desire  to 
distinguish  details,  as  where  work  is  being  done,  at  the  reading- 
table,  work  bench,  dining-table  etc.,  while  the  general  illumina- 
tion is  merely  for  orientation  in  the  space,  and  thus  may  be  of 
lower  intensity,  and  for  reasons  of  economy,  and  also  physio- 
logical reasons,  should  be  of  lower  intensity. 

We  thus  have  to  distinguish  between  local  or  concentrated, 
and  general  or  uniform,  illumination,  and  a  combination  of 
both,  and  have  to  distribute  the  light  flux  in  accordance  there- 
with, that  is,  produce  a  high  flux  density  at  the  points  or  areas 
requiring  high  concentrated  illumination,  a  low  and  uniform 
flux  density  throughout  the  remaining  space. 

This  can  be  done  by  choosing  a  light  source  of  the  proper 
distribution  curve,  as,  for  instance,  in  street  illumination  a  lamp 


ILLUMINATION  AND  ILLUMINATING  ENGINEERING.     261 

giving  most  of  the  light  flux  between  the  horizontal  and  20  deg. 
below  the  horizontal;  in  many  cases  of  indoor  illumination 
a  light  source  giving  most  of  the  light  between  the  vertical 
and  an  angle  of  from  30  to  60  deg.  from  the  vertical — depending 
on  the  diameter  of  the  area  of  concentrated  illumination  and 
the  height  of  the  illuminant  above  it.  It  can  also  be  done  by 
modifying  or  directing  the  light  flux  of  the  illuminant  by  reflec- 
tion or  diffraction  and  diffusion,  either  from  walls  and  ceilings 
of  the  illuminated  area,  or  by  attachments  to  the  illuminant, 
as  reflectors,  diffusing  globes,  diffracting  shades,  etc.  Further- 
more, the  required  flux  distribution  can  be  secured  by  the  use 
of  a  number  of  illuminants,  and  with  a  larger  area  this  usually 
is  necessary.  Frequently  the  desired  flux  distribution  is  pro- 
duced by  using  an  illuminant  giving  more  light  flux  than  neces- 
sary, and  destroying  the  excess  of  flux  in  those  directions  where 
it  is  not  wanted,  by  absorption.  Obviously  this  arrangement 
is  uneconomical  and  thus  bad  illuminating  engineering;  the 
desired  flux  distribution  should  be  secured  economically,  that 
is,  without  unnecessary  waste  of  light  flux  by  absorption,  and 
this  usually  can  be  done  by  a  combination  of  a  number  of  light 
sources  of  suitable  distribution  curves.  The  most  economical 
method  of  securing  the  desired  distribution  curve  obviously  is 
to  choose  a  light  source  coming  as  near  to  it  as  possible,  and 
then  modifying  it  by  reflection  or  diffraction. 

113.  Thus  far,  the  problem  is  one  of  physics,  and  the  result, 
that  is,  the  objective  illumination,  can  be  measured  by  photometer 
or  luminometer,  and  thus  checked.  The  duty  of  the  illuminat- 
ing engineer,  however,  does  not  end  here,  but  with  the  same 
objective  illumination,  that  is,  the  same  distribution  of  light 
flux  throughout  the  entire  illuminated  area,  as  measured  by 
photometer,  the  illumination  may  be  very  satisfactory,  or  it 
may  be  entirely  unsatisfactory,  depending  on  whether  the  physio- 
logical requirements  are  satisfied  or  are  violated ;  and  very  often 
we  find  illuminations  which  seem  entirely  unsatisfactory,  tiring, 
or  uncomfortable,  but  when  judged  by  the  density  and  the 
distribution  of  the  light  flux,  should  be  satisfactory.  Even 
numerous  commercial  illuminants,  designed  to  give  suitable 
distribution  curves,  fail  to  do  justice  to  their  light  flux  and 
its  distribution,  by  violating  fundamental  physiological  require- 
ments. 


262          RADIATION,  LIGHT,  AND  ILLUMINATION. 

The  physiological  problems  of  illumination,  that  is,  the  effects 
entering  between  the  objective  distribution  of  light  flux  in  space, 
and  the  subjective  effects  produced  on  the  human  eye,  thus  are 
the  most  important  with  which  the  illuminating  engineer  has  to 
deal,  and  the  first  feature  which  must  be  recognized  is  that  the 
objective  illumination,  as  measured  by  the  photometer,  is  no 
criterion  of  the  subjective  illumination,  that  is,  the  physiological 
effect  produced  by  it,  as  regard  to  clearness,  comfort  and  satis- 
faction, and  it  is  the  subjective  illumination  by  which  the  success 
of  an  illuminating  engineering  problem  is  judged. 

The  most  important  physiological  effects  are : 

(a)  The  contraction  of  the  pupil.  The  pupil  of  the  eye  auto- 
matically reacts,  by  contraction,  on  high  brilliancy  at  or  near 
the  sensitive  spot,  that  is,  the  point  of  the  retina,  on  which  we 
focus  the  image  of  the  object  at  which  we  look,  and  to  a  some- 
what lesser  extent  on  high  brilliancy  anywhere  else  in  the  field 
of  vision.  If,  therefore,  points  or  areas  of  high  brilliancy  are 
in  the  field  of  vision,  especially  if  near  to  objects  at  which  we 
look,  the  pupil  contracts  the  more  the  higher  the  brilliancy, 
and  thereby  reduces  the  amount  of  light  flux  which  enters  the 
eye,  that  is,  produces  the  same  result  as  if  the  objective 
illumination  had  been  correspondingly  reduced,  intensified  by 
the  uncomfortable  effect  of  seeing  high  brilliancy.  The  exist- 
ence of  points  of  high  brilliancy  in  the  field  of  vision  thus  results 
in  a  great  waste  of  light  flux,  and  additional  discomfort,  and,  for 
satisfactory  illumination,  points  of  high  brilliancy  thus  must 
be  kept  out  of  the  field  of  vision.  Light  sources  of  high  brilliancy 
must  be  arranged  so  that  they  cannot  directly  be  seen,  but  the 
illumination  accomplished  by  the  light  reflected  from  ceilings, 
etc.,  or  from  reflectors  attached  to  the  illuminant:  indirect  light- 
ing; or  at  least  the  light  sources  should  be  located  where  we 
are  rarely  liable  to  look  at  them,  that  is,  with  moderate-sized 
rooms,  at  or  near  the  ceilings.  Or  light  sources  of  moderate 
intrinsic  brilliancy  should  be  used,  as  the  Moore  tube,  the 
mercury  lamp,  the  Welsbach  mantel.  Or,  with  illuminants  of 
high  brilliancy,  as  the  electric  arc,  the  incandescent  lamp 
(especially  the  tungsten  filament),  etc.,  the  brilliancy  of  the 
illuminant  must  be  reduced  by  enclosing  it  with  a  diffusing  or 
diffracting  globe  or  shade,  as  an  opal  or  frosted  or 
holophane  globe,  etc. 


ILLUMINATION  AND  ILLUMINATING  ENGINEERING.      263 

No  illumination,  however,  can  be  satisfactory  in  which  the 
eye  at  any  time  can  be  exposed  to  the  direct  rays  from  a  tungsten 
filament  or  an  arc.  While  the  methods  of  removing  the  high 
brilliancy  of  the  illuminant  usually  involve  a  considerable  loss  of 
light  flux,  by  absorption  at  the  refracting  surface,  in  the  frosted 
or  opal  globe,  etc.,  and  the  objective  illumination  thus  is  de- 
creased, if  the  methods  of  reducing  the  brilliancy  are  anywhere 
reasonably  arranged,  the  light  flux  entering  the  eye,  and  thus 
the  subjective  illumination,  is  increased,  and  often  very  greatly. 
Thus  while  frosting  an  incandescent  lamp  decreases  its  light 
flux  by  about  15  per  cent,  in  spite  thereof  usually  more  light 
flux  enters  the  eye  from  the  frosted  lamp  than  from  a  clear  glass 
lamp  at  the  same  distance. 

It  is,  therefore,  inefficient  to  use  illuminants  of  high  brilliancy 
in  the  field  of  vision,  and  in  addition  makes  the  illumination 
uncomfortable  and  thereby  unsatisfactory.  Physiologically  the 
brilliancy  of  the  light  source  thus  is  one  of  the  most  important 
quantities. 

114.  (6)  Fatigue.  When  exposed  to  fairly  high  light  flux  den- 
sity, that  is,  high  illumination,  the  nerves  of  the  eye  decrease 
in  sensitivity,  by  fatigue,  and  inversely,  in  lower  illumination 
or  in  darkness,  increase  in  sensitivity.  This  reaction,  or  adjust- 
ment of  the  sensitivity  of  the  nerves  of  vision  to  different  intensi- 
ties of  illumination,  enables  us  to  see  equally  well  in  illuminations 
varying  in  intensity  by  more  than  10,000  to  1  (as  daylight  and 
artificial  light).  Thus,  when  entering  a  well-illuminated  room 
from  the  darkness,  it  first  appears  glaring,  until  gradually 
the  impression  fades  down  to  normal.  Inversely,  coming  from 
a  well-lighted  room  into  a  space  of  much  lower  illumination,  it 
first  appears  practically  dark,  until  gradually  the  eye  adjusts 
itself,  that  is,  the  nerves  of  vision  increase  in  sensitivity  by  their 
rest,  and  then  we  again  see  fairly  well. 

Fatigue  and  contraction  of  the  pupil  thus  are  similar  in  their 
action,  in  that  they  reduce  the  physiological  effect  for  high 
intensities.  The  contraction  of  the  pupil,  however,  is  almost 
instantaneous,  and  is  a  protective  action  against  excessive  bril- 
liancies in  the  field  of  vision,  while  the  fatigue  is  a  gradual 
adjustment  to  the  average  intensity  of  illumination,  within  the 
operating  range  of  the  human  eye. 

By  exposure  for  a  considerable  period  to  the  fairly  high  illumi- 


264  RADIATION,  LIGHT,  AND  ILLUMINATION. 

nation  required  when  working  by  artificial  light,  the  sensitivity 
of  the  eye  decreases,  the  illumination  appears  less  bright,  and 
thus  a  higher  illumination  is  required  than  would  be  sufficient 
in  the  absence  of  fatigue,  and  the  continuous  use  and  absence 
of  rest  cause  the  sensation  of  strain,  that  is,  irritation  or  an 
uncomfortable  feeling,  as  especially  noticeable  when  working 
or  reading  for  a  considerable  length  of  time  in  rooms  having  a 
high  uniform  intensity  of  illumination,  as  meeting-rooms,  some 
libraries,  etc.  If,  however,  the  eye  can  rest  even  momentarily, 
by  a  change  to  lower  intensity  of  illumination,  fatigue  is  decreased, 
never  becomes  as  complete  and  uncomfortable,  and  the  concen- 
trated illumination  of  the  working-table  appears  brighter  than 
it  would  without  the  possibility  of  rest. 

A  room  having  a  uniform  intensity  of  illumination  thus  appears 
glaring  and  uncomfortable,  and  for  satisfactory  illumination 
it  is  necessary  not  only  to  provide  a  sufficiently  high  intensity 
at  the  place  where  needed,  but  it  is  just  as  necessary  to  keep 
the  intensity  of  illumination  as  low  as  permissible,  wherever 
it  is  not  needed,  so  as  to  afford  to  the  eye  rest  from  the  fatigue. 
In  some  cases,  as  meeting-halls,  schoolrooms,  this  may  not  be 
possible,  but  a  uniform  high  intensity  required,  to  be  able  to 
work  or  read  anywhere  in  the  room.  Where,  however,  it  is  not 
necessary,  it  is  not  merely  uneconomical  to  provide  a  uniform 
high  intensity  of  illumination,  but  it  is  an  illuminating  engineer- 
ing defect,  and  a  high  intensity  should  be  provided,  as  concen- 
trated illumination,  only  at  those  places  where  required,  as 
at  the  reading-tables  of  the  library,  but  the  general  illumination 
should  be  of  lower  intensity.  While  we  rarely  realize  the  cause, 
we  feel  the  superiority  of  the  combination  of  high  concentrated 
and  lower  general  illumination,  by  speaking  of  such  illumination 
as  home-like,  restful,  etc.  Especially  in  places  where  considerable 
work  has  to  be  done  by  artificial  illumination,  as  in  libraries, 
factories,  etc.,  to  get  satisfactory  results,  it  is  important  to 
consider  this  effect  of  fatigue,  and  to  properly  combine  a  moder- 
ately low  general  illumination  with  a  local  higher  intensity  of 
illumination  at  the  places  of  work.  The  latter  can  usually  be 
given  by  a  light  source  having  a  downward  distribution,  located 
sufficiently  high  above  the  place  of  work.  The  average  standing 
or  reading  lamp,  however,  generally  is  not  sufficiently  high  to 
accomplish  the  result.  Obviously,  in  such  local  illumination, 


ILLUMINATION  AND  ILLUMINATING  ENGINEERING.     265 

the  brilliancy  of  the  illumination  must  be  kept  low,  as  discussed 
above. 

Of  considerable  importance  regarding  fatigue  is  the  quality, 
that  is,  the  color,  of  the  light :  fatigue  at  high  intensities  occurs 
far  more  with  yellow  and  orange  rays  than  with  white  light, 
and  very  little  with  green  and  bluish-green  light.  Thus,  in  arti- 
ficial illumination,  in  which  practically  always  the  yellow  and 
orange  rays  greatly  preponderate,  the  question  of  fatigue  is  far 
more  important  than  with  the  bluish-white  diffused  daylight, 
and  the  irritating  effects  of  fatigue  thus  are  mostly  felt  with 
artificial  illumination. 

115.  (c)  Differences.  Objects  are  seen  and  distinguished  by 
differences  in  quality,  that  is,  color,  and  in  intensity,  that  is, 
brightness,  of  the  light  reflected  by  them.  If  there  were  no 
differences  in  color  or  in  intensity  throughout  the  field  of  vision, 
we  would  see  light  but  would  not  distinguish  objects.  Therefore, 
in  good  illumination,  the  differences  in  color  and  in  intensity 
should  be  sufficiently  high  to  see  clearly  by  them,  but  still  limited 
so  as  not  to  preponderate  to  such  extent  as  to  distract  the  atten- 
tion from  smaller  differences.  The  differences  in  intensity, 
to  give  distinction,  should  be  high,  but  at  the  same  time  are 
limited  by  the  phenomena  of  fatigue  and  of  the  contraction 
of  the  pupil:  the  minimum  intensity  must  still  be  sufficiently 
high  to  see  clearly,  and  the  maximum  intensity  not  so  high  as 
to  cause  fatigue  and  contraction  of  the  pupil,  much  beyond 
that  corresponding  to  the  average  intensity,  otherwise  the  vision 
becomes  indistinct  and  unsatisfactory,  and  uncomfortable  by 
too  much  contrast;  that  is,  the  intensity  differences  must  give 
a  sufficient,  but  not  an  excessive,  contrast,  if  the  illumination  is 
to  be  satisfactory. 

Differences  in  quality,  that  is,  in  color,  are  to  a  limited  extent 
only  under  the  control  of  the  illuminating  engineer.  In  some 
cases  the  illuminating  engineer  can  control  or  advise  regarding 
the  color  of  objects,  as  the  walls,  ceilings,  etc.  In  most  cases, 
however,  the  absolute  color  of  the  illuminated  objects  is  not  within 
the  control  of  the  illuminating  engineer:  for  instance,  in  street 
lighting,  the  color  of  the  street  surface,  its  surroundings,  as 
vegetation,  houses,  etc.,  are  fixed  and  cannot  be  changed  for 
effects  of  illumination.  So  also  in  most  cases  of  indoor  illumina- 
tion. To  some  extent,  however,  the  subjective  color  can  be  con- 


266  RADIATION,  LIGHT,  AND  ILLUMINATION. 

trolled  by  the  choice  of  the  proper  shade  of  light,  and  thereby 
slight  color  differences  increased  and  made  more  distinct,  or 
decreased  and  thus  obliterated.  For  instance,  the  color  resulting 
from  age  and  dirt  is  usually  the  color  of  carbon  and  of  iron, 
yellowish  brown  or  reddish  brown,  that  is,  colors  at  the  long 
wave  end  of  the  spectrum.  Spots  and  blemishes  due  to  dirt 
or  age,  thus  are  made  more  distinct  by  using  an  illuminant  defi- 
cient in  the  long  waves  of  light,  as  the  mercury  lamp,  while  in- 
versely they  are  decreased  by  using  a  reddish-yellow  illuminant, 
as  the  incandescent  lamp  or  the  candle.  Thus  the  white  arc 
lamp  and  still  more  so  the  bluish-green  mercury  lamp  shows 
blemishes  and  slight  color  differences  of  age  and  dirt  harsh  and 
exaggerated,  while  the  yellow  light  softens  them  and  makes 
them  disappear;  and  while,  for  a  ballroom,  the  yellow  light 
is  thus  preferred,  and  the  mercury  arc  or  even  the  ordinary 
white  carbon  arc  would  give  a  harsh  and  disagreeable  effect, 
inversely  the  yellow  light  would  be  unsuitable  where  such  slight 
differences  should  be  distinguished.  It  is  therefore  essential 
for  the  illuminating  engineer  to  choose  as  far  as  it  is  feasible  the 
proper  color  of  light,  and  an  otherwise  good  illumination  may  be 
spoiled  by  using  too  white  or  too  yellow  a  light. 

The  main  distinction  of  objects,  however,  is  due  to  differences 
in  intensity  or  brightness,  and,  for  producing  these,  the  shadows 
are  of  foremost  assistance,  and  indeed  the  differences  of  inten- 
sity, by  which  we  see  objects,  are  to  a  large  extent  those  due 
shadows.  The  study  of  the  shadow  thus  is  one  of  the  most 
important  subjects  of  illuminating  engineering.  If  we  have  no 
shadows,  but  a  perfectly  diffused  illumination,  even  if  the 
intensity  of  illumination  is  sufficient,  the  illumination  is  unsatis- 
factory, as  we  lose  the  assistance  of  the  shadows  in  distinguishing 
objects,  and  therefore  find  seeing  more  difficult,  the  illumination 
restless  and  uncomfortable. 

The  use  of  shadows  for  illumination  requires  that  we  must 
have  directed  light,  that  is,  light  coming  from  one  or  a  number 
of  sources,  and  thus  causing  shadows,  and  not  merely  diffused 
illumination,  that  is,  light  coming  from  all  directions  and  thus 
causing  no  shadows.  While,  however,  in  general  perfectly  dif- 
fused illumination  is  unsatisfactory,  an  illumination  having  only 
directed  light  is  also  unsatisfactory.  If  the  light  is  all  directed, 
as  from  a  single  arc,  the  shadows  are  absolutely  black,  we  can- 


ILLUMINATION  AND  ILLUMINATING  ENGINEERING.     267 

not  see  anything  in  them,  and,  in  attempting  to  see  the  objects 
in  the  shadows,  the  illumination  becomes  tiring  to  the  eyes, 
irritating  and  restless. 

For  satisfactory  illumination,  it  therefore  is  necessary  to 
have  sufficient  directed  light  to  mark  the  edge  of  the  objects 
by  their  shadow,  and  thereby  improve  distinction,  but  at  the 
same  time  sufficient  diffused  light  to  see  clearly  in  the  shad- 
ows; that  is,  a  proper  proportion  of  directed  and  diffused  light  is 
necessary. 

In  cases  in  which  all  the  objects  assume  practically  the  same 
color,  as  in  flour  mills  or  foundries,  a  diffused  illumination  without 
shadows  would  make  the  illumination  so  bad  as  to  be  practically 
useless.  In  other  cases,  as  a  drafting-room,  where  all  the  objects 
requiring  distinction  are  in  one  plane,  as  the  drafting  board,  and 
the  distinction  is  exclusively  by  differences  of  color  and  intensity, 
but  not  by  shadows,  a  perfectly  diffused  illumination  is  required, 
and  shadows  would  be  objectionable  and  misleading,  and  this 
is  one  of  the  cases  where  directed  light  is  objectionable. 

While  with  a  single  light  source  all  the  light  issuing  from  it 
is  directed  light,  by  using  a  number  of  illuminants,  the  overlap 
of  their  light  fluxes  causes  more  or  less  light  to  reach  objects 
from  all  directions,  and  thereby  gives  the  effect  of  diffused  light, 
except  at  those  places  where  the  shadows  cast  by  the  different 
light  sources  coincide,  and  by  proper  positions  of  sufficient 
numbers  of  light  sources  this  can  be  avoided.  The  use  of  a 
number  of  light  sources  thus  offers  a  means  of  increasing  the 
proportion  of  diffused  to  directed  light. 

116.  It  is  not  sufficient,  however,  to  have  merely  a  combination 
of  diffused  and  directed  light  in  the  proper  proportion,  but  the 
direction  of  the  latter  also  is  of  importance.  In  some  simple 
cases  this  is  obvious,  as,  in  writing,  the  directed  light  should 
be  from  in  front  on  the  left  side  above  the  table,  so  as  not  to 
cast  the  shadow  on  the  work.  The  purpose  of  the  shadow  in 
illumination  is  to  mark  the  edge  of  the  object,  and  its  height 
by  the  length  of  the  shadow.  The  shadow,  therefore,  should 
not  extend  too  far  from  the  object  to  which  it  is  related,  other- 
wise it  loses  its  close  relation  to  it  and  becomes  misleading  and 
thereby  interferes  with  good  illumination.  Thus  the  directed 
light  should  come  from  above,  that  is,  in  a  direction  making  a 
considerable  angle  with  the  horizontal,  so  as  to  limit  the  length 


268  RADIATION,  LIGHT,  AND  ILLUMINATION. 

of  the  shadow  without,  however,  being  vertical,  as  the  latter 
would  largely  obliterate  shadows.  Perhaps  an  angle  of  45  to 
60  degrees  with  the  horizontal  would  be  most  satisfactory. 
The  practically  horizontal  shadows  cast  in  the  usual  form 
of  street  lighting  therefore  are  not  satisfactory  for  best  illumi- 
nation. 

The  number  of  shadows  is  of  less  importance.  While  in  nature 
objects  have  one  shadow  only,  cast  by  the  sun,  indoors  we  are 
familiar  with  seeing  several  shadows  due  to  the  diffused  day- 
light from  several  windows.  Of  high  importance,  however,  is 
the  shape  of  the  illuminant,  in  so  far  as  it  determines  the  outer 
edge  of  the  shadow.  The  purpose  of  the  shadow  is  to  give  an 
intensity  difference  at  the  edge  of  the  object,  and  thereby  make 
it  easier  to  see  the  object.  The  shadow,  however,  has  another 
edge,  its  outer  end,  and  that  we  should  not  see,  as  no  object 
ends  there,  or  at  least  it  must  be  such  that  it  cannot  be  mistaken 
for  the  edge  of  an  object.  The  problem  thus  is  not  merely  to 
provide  sufficient  directed  light  to  cast  a  shadow,  but  the  shadow 
should  be  such  that  only  one  side,  at  the  edge  of  the  object,  is 
sharply  defined,  while  the  other  edge  of  the  shadow,  which  ter- 
minates on  the  flat  surrounding  surface,  should  gradually  fade 
or  blur.  If  we  have  to  look  closely  to  determine  that  the  outer 
edge  of  the  shadow  is  not  the  edge  of  another  object,  the  strain 
of  distinguishing  between  the  edge  of  an  object  and  the  edge 
of  a  shadow  makes  the  illumination  uncomfortable  and  thus 
unsatisfactory.  In  the  shadows  cast  by  a  single  arc  in  a  clear 
glass  globe,  this  difficulty  of  distinguishing  between  the  edge 
of  a  shadow  and  the  edge  of  an  object  is  especially  marked,  and, 
combined  with  the  invisibility  of  objects  in  the  shadow,  makes 
such  shadows  appear  on  first  sight  like  ditches  or  obstructions. 

In  the  use  of  shadows  in  illuminating  engineering  it  thus  is 
necessary  to  have  the  outer  edge  of  the  shadows  blur  or  gradually 
fade,  and  this  requires  that  the  source  of  directed  light  be  not  a 
point,  but  a  sufficiently  large  area  to  scatter  the  light  at  the  outer 
edge  of  the  shadow,  preferably  even  more  than  is  the  case 
with  the  shadows  cast  by  the  sun.  This  requires  enclosing 
the  illuminant  by  a  fairly  large  opal  globe  or  other  similar 
device;  that  is,  have  the  light  issue  from  a  fairly  large  luminous 
area. 

It  must  be  recognized  that  the  proper  treatment  of  the  shadows 


ILLUMINATION  AND  ILLUMINATING  ENGINEERING.     269 

is  one  of  the  most  important  problems  determining  the  success 
or  failure  of  an  illumination. 

117.  Color  sensitivity.  The  maximum  of  sensitivity  of  the 
eye  shifts  with  decreasing  illumination  from  yellow  to  bluish 
green,  and  where  a  low  intensity  of  illumination  is  used,  as  in 
street  lighting,  a  source  of  light  which  is  rich  in  the  shorter 
waves,  that  is,  a  white  light,  is  superior  in  its  physiological 
illuminating  value  to  a  yellow  light  of  the  same  or  even 
higher  light  flux,  while  inversely  at  high  values  of  illumina- 
tion, as  for  decorative  purposes,  the  yellow  light  is  more 
effective. 

Therefore  it  is  a  mistake  to  choose  a  yellow  light  source  for 
illumination  of  very  low  intensity,  or  a  white  or  bluish-green 
light  for  illumination  attempting  high  intensity  effects.  Thus, 
for  the  average  street  lighting  of  American  cities,  the  white  arc 
is  superior  to  the  yellow  flame  arc,  but,  to  produce  a  glare  of  light, 
the  latter  would  be  superior. 

While  there  are  further  physiological  effects  which  are  of  im- 
portance in  illuminating  engineering,  the  above  four  may  illus- 
trate the  long  step  which  exists  between  the  distribution  of  the 
light  flux  as  measurable  by  the  photometer,  and  the  success  or 
failure  of  the  illumination  represented  by  it. 

The  requirements  of  satisfactory  illumination  can  thus  be 
grouped  in  two  main  classes,  referring  respectively  to  economy 
and  to  comfort,  and  the  characteristics  are: 

(1)  General  or  uniform,  and  local  or  concentrated  illumination, 
and  combination  of  both.    This  is  of  importance  for  economy :  to 
avoid  the  production  of  unnecessary  light  flux;  and  comfort:  to 
reduce  the  effect  of  fatigue. 

(2)  Diffused  and  directed  illumination,  and  combinations  of 
both,  and  the  theory  of  the  shadow.    This  is  of  importance  for 
the  comfort  of  illumination,  in  securing  clearest  distinction. 

(3)  Quality  or  color  of  light,  of  importance  in  economy,  to 
suit  the  color  to  the  intensity  of  illumination,  and  to  comfort, 
in  increasing  or  softening  differences  in  color  shades. 

(4)  Massed  and  distributed  illumination,  as  controlling  the 
distribution  of  the  light  flux,  and  thereby  the  economy  and  also 
the  diffusion. 

(5)  Direct  illumination   and   indirect  illumination,   shaded, 
diffracted,  diffused,  or  reflected  light,  in  its  relation  to  the  bril- 


270  RADIATION,  LIGHT,  AND  ILLUMINATION. 

liancy  of  the  light  source,  and  thereby  the  effect  of  the  contraction 
of  the  pupil,  on  economy  and  comfort. 
Some  of  the  common  mistakes  made  in  illumination  are : 

(1)  Unsatisfactory  proportion  of  general  and  of  concentrated 
light. 

(2)  Exposure  of  high  brilliancies  in  the  field  of  vision,  as  naked 
filaments. 

(3)  Unsuitable  proportion  of  diffused  and  directed  light. 

(4)  Improper  direction  of  directed  light  and  thereby  improper 
length  of  shadows. 

(5)  Sharp  edges  of  shadows. 

In  order  to  illustrate  the  preceding  principles,  some  typical 
cases  may  be  considered : 

(a)   Domestic  lighting. 

118.  Domestic  lighting  usually  requires  a  combination  of  a 
concentrated  illumination  of  fairly  high  intensity  locally  at  the 
work-table,  dining-table,  etc.,  and  a  general  illumination  of  low 
intensity,  to  secure  comfort  and  economy.  Occasionally,  as  in 
halls,  etc.,  the  local  lighting  is  absent  and  only  general  illumina- 
tion required,  while  for  instance  in  a  sick  room  the  general  illumi- 
nation is  absent  and  only  local  illumination  required. 

In  this  illumination  the  proportion  between  directed  and  dif- 
fused light  should  be  such  as  to  give  the  proper  effect  of  shadows. 
The  problem  of  domestic  illumination  thus  is  to  produce  a  defi- 
nite distribution  of  light  flux  density,  with  a  definite  proportion 
between  diffused  and  directed  light.  If  we  deviate  from  the 
proper  proportion  on  one  side,  the  room  appears  cold  and  uncom- 
fortable; if  we  deviate  in  the  other  direction,  it  appears  dark  and 
gloomy. 

The  light  issuing  directly  from  a  single  illuminant  is  directed 
light;  the  light  issuing  from  a  number  of  illuminants  is  diffused 
in  proportion  to  the  number  of  sources  by  the  overlap  of  the  light 
fluxes  of  the  illuminants.  The  light  reflected  from  walls  and 
ceilings  is  diffused  light.  The  proportion  between  the  light 
reflected  from  walls  and  ceilings,  or  the  indirect  light,  and  the 
direct  light  from  the  illuminants,  varies  with  the  reflecting  power 
of  walls  and  ceilings,  that  is,  their  brightness  or  darkness.  The 
proportion  between  directed  and  diffused  light  thus  can  be 
changed,  and  the  diffused  light  increased  by  increasing  the  num- 
ber of  illuminants,  and  also  by  increasing  the  brightness  of  walls 


ILLUMINATION  AND  ILLUMINATING  ENGINEERING.     271 

and  ceilings.  With  a  given  brightness  of  walls  and  ceilings,  the 
desired  distribution  of  the  light  flux — a  local  high  and  general  low 
intensity  —  can  be  produced  by  a  single  illuminant  having  the 
proper  distribution  curve  of  light  flux.  In  this  case,  however, 
usually  we  get  too  much  directed,  and  not  enough  diffused,  light. 
The  same  distribution  of  light  flux  can  be  produced  by  a  number 
of  illuminants  properly  located :  nearer  together  for  the  local  than 
for  the  general  illumination.  In  the  latter  case  we  get  more 
diffused  and  less  directed  light,  and  thus  by  choosing  the  number 
of  light  sources  it  is  possible,  with  any  given  brightness  of  walls 
and  ceilings,  to  get  the  desired  distribution  of  light  flux  and  at 
the  same  time  the  proper  proportion  of  directed  and  diffused 
light.  With  a  different  brightness  of  walls  and  ceilings,  the  dis- 
tribution curve  of  a  single  light  source,  required  to  give  the 
desired  light  flux  distribution,  is  correspondingly  changed,  and, 
the  lighter  the  walls  and  ceilings,  the  more  light  is  reflected,  giving 
a  diffused  general  illumination,  and  thus  less  direct  light  from  the 
illuminant  is  required  for  the  general  illumination.  With  in- 
creasing reflecting  power  of  walls  and  ceilings,  the  proportion  of 
diffused  light  increases,  and  the  number  of  light  sources  which 
are  required  to  give  the  proper  proportion  between  directed  and 
diffused  light  is  decreased,  and  inversely  it  is  increased  with 
increasing  darkness  of  walls  and  ceiling.  Therefore,  in  a  room 
with  light  walls,  a  smaller  number  of  light  sources  is  required  for 
good  illumination  than  in  a  room  with  dark  walls,  assuming  the 
same  intensity  of  local  and  of  general  illumination. 

119.  The  problem  of  domestic  illumination:  to  get  a  certain 
distribution  of  illumination,  with  a  definite  proportion  between 
directed  and  diffused  light,  thus  leaves  one  independent  variable 
—  the  brightness  of  walls  and  ceilings.  This  is  necessary,  as  the 
problem  of  domestic  illumination  is  twofold:  to  get  the  proper 
illumination  by  means  of  the  daylight,  and  also  to  get  it  for 
artificial  illumination.  During  daytime,  the  windows  are  the 
source  of  light,  the  directed  light  issues  from  the  windows,  the 
diffused  light  from  the  walls  and  ceilings  and  by  the  overlap  of 
the  light  from  several  windows.  The  proper  distribution  between 
local  and  general  illumination  during  daytime,  and  at  the  same 
time  the  proportion  of  directed  and  diffused  light,  thus  deter- 
mines the  number  of  windows  and  the  brightness  of  walls  and 
ceilings,  in  the  manner  as  discussed  before. 


272  RADIATION,  LIGHT,  AND  ILLUMINATION. 

As  the  reflecting  power  of  walls  and  ceilings  is  fixed  by  day- 
light considerations,  it  cannot  be  chosen,  or  at  least  only  to  a 
limited  extent,  by  considerations  of  artificial  illumination,  but,  as 
found  above,  this  is  not  necessary,  since  by  a  combination  of  a 
suitable  number  of  light  sources  of  proper  distribution  curves 
the  problem  of  artificial  illumination  may  be  solved.  To  some 
extent,  due  to  the  quality  of  artificial  light  and  daylight,  the  walls 
can  give  a  different  reflecting  power  for  the  one  than  for  the 
other.  As  artificial  light  is  deficient  in  blue  and  green,  a  bluish 
or  greenish  shade  of  walls  and  ceilings  gives  them  a  greater  reflect- 
ing power  for  daylight  than  for  artificial  light  — which  usually 
is  desirable  —  and  inversely  with  a  reddish-yellow  shade. 

(b)   Street  Lighting. 

120.  The  problem  of  street  illumination  is  to  produce  a  uni- 
form low  intensity.  For  reasons  of  economy,  the  intensity  must 
be  low,  at  least  in  American  cities,  in  which  the  mileage  of  streets, 
for  the  same  population,  usually  is  many  times  greater  than  in 
European  cities,  and,  at  the  same  time,  the  same  type  of  illumi- 
nant  is  usually  required  for  the  entire  area  of  the  city.  The  low 
intensity  of  illumination  requires  the  quality  of  light  which  has 
the  highest  physiological  effect  at  low  densities,  that  is,  white 
light,  and  excludes  the  yellow  light  as  physiologically  inefficient 
for  low  intensities.  Still  better  would  be  the  bluish  green  of 
the  mercury  lamp,  but  is  not  much  liked,  due  to  its  color.  Quite 
satisfactory  also  is  the  greenish  yellow  of  the  Welsbach  mantel 
for  these  low  intensities.  The  American  practice  of  preferring 
the  white  light  of  the  carbon  or  magnetite  arc  thus  is  correct 
and  in  agreement  with  the  principles  of  illumination,  and  the 
yellow-flame  arc  can  come  into  consideration  —  even  if  it  were  not 
handicapped  by  the  necessity  of  frequent  trimming  — only  in 
those  specific  cases  where  a  high  intensity  of  illumination  is 
used,  as  would  be  only  in  the  centers  of  some  large  cities. 

Uniformity  of  illumination  is  specially  important  in  street  light- 
ing, where  the  observer  moves  along  the  street,  and,  due  to  the 
low  intensity,  the  decrease  of  subjective  illumination  by  fatigue 
is  especially  objectionable.  For  a  street  illuminant,  a  distribu- 
tion curve  is  required  which  gives  a  maximum  intensity  some- 
what below  the  horizontal,  no  light  in  the  upper  hemisphere,  and 
very  little  downward  light.  Street  lamps  therefore  should  be 
judged  and  compared  by  the  illumination  given  midways  be- 


ILLUMINATION  AND  ILLUMINATING  ENGINEERING.     273 

tween  adjacent  lamps,  or  at  the  point  of  minimum  intensity,  or, 
in  other  words,  by  the  intensity  in  a  direction  approximately 
10  deg.  below  the  horizontal.  This  also  is  in  agreement  with 
American  practice.  However,  it  is  very  important  that  the 
downward  intensity  be  very  low,  and  in  this  respect  it  is  not 
always  realized  that  the  light  thrown  downward  is  not  merely  a 
waste  of  light  flux,  but  is  harmful  in  producing  a  glaring  spot  at 
or  near  the  lamp  and,  by  the  fatigue  caused  by  it,  reducing  the 
effective  illumination  at  the  minimum  point  between  the  lamps. 
Most  objectionable  in  this  respect  is  the  open  direct  current  car- 
bon arc  and  those  types  of  lamps  giving  a  downward  distribution, 
but  even  with  the  enclosed  arc  lamp  the  distribution  of  light  on 
the  street  surface  is  still  far  from  uniform,  and  the  intensity 
too  high  near  the  lamp,  and  in  this  respect  improvements  are 
desirable. 

121.  The  greatest  defects  of  the  present  street  illumination, 
which  frequently  makes  it  inferior  in  subjective  illumination  even 
to  the  far  lower  illumination  given  by  the  full  moon,  are  the 
absence  of  diffused  light,  and  especially  the  improper  direction 
and  termination  of  the  shadows,  and  also  the  high  brilliancy  of 
the  illuminant.  The  light  of  the  usual  street  lamp  is  practically 
all  directed  light,  issuing  in  a  nearly  horizontal  direction  from  a 
point  source.  Thus  the  shadows  are  far  longer  than  permissible, 
and  terminate  sharply  and  without  blur;  objects  in  the  shadows 
are  practically  invisible,  and  the  end  of  the  shadow  looks  like  the 
edge  of  an  object,  thus  producing  a  misleading  effect,  which 
results  in  unsatisfactory  illumination.  To  give  a  somewhat 
better  direction  to  the  light  requires  considerable  increase  of  the 
height  of  the  lamp  above  the  street  surface.  This  also  would 
essentially  decrease  the  intensity  of  illumination  below  and  near 
the  lamp, without  appreciably  affecting  the  intensity  at  the 
minimum  point,  and  thus  would  give  a  more  uniform  and  thereby 
better  illumination.  No  valid  reason  usually  exists  against 
greatly  increasing  the  height  of  the  lamps,  except  that  of  the 
greater  cheapness  of  short  lamp  posts,  which  is  hardly  justifiable. 
It  is,  however,  more  difficult  to  give  a  proper  blur  to  the  ends  of 
shadows,  so  as  to  distinguish  them  from  edges  of  objects.  This 
would  require  an  increase  of  the  surface  of  the  illuminant,  by 
opal  or  frosted  globe,  etc.  Enclosing  the  arc  by  an  opal  globe, 
however,  scatters  the  light  more  uniformly  in  all  directions,  and 


274  RADIATION,  LIGHT,  AND  ILLUMINATION. 

thereby  spoils  the  distribution  curve,  and  interferes  with  the 
required  uniformity  of  illumination :  with  an  opal  globe,  the 
intensity  in  the  downward  direction  does  not  differ  very  much 
from  that  in  the  horizontal,  while  with  lamps  20  feet  above  the 
street  level,  and  at  distances  of  200  feet  from  each  other,  the 
downward  intensity  for  uniform  illumination  should  be  not  much 
more  than  one-twenty-fifth  of  that  under  an  angle  of  sin  $  = 

20 

—  =  0.2;  or  12  deg.  below  the  horizontal.    Very  much  better  is 

-L  \J{J 

the  effect  of  a  frosted  or  sand-blasted  globe.  The  best  way  of 
maintaining  a  proper  distribution  curve  and  at  the  same  time 
diffusing  the  light,  so  as  to  reduce  its  brilliancy  and  blur  the 
shadows,  appears  the  use  of  prismatic  diffraction,  on  the  principle 
of  the  Fresnel  lenses  of  lighthouses  (holophane).  Obviously, 
where  the  lamps  are  close  together,  as  in  the  center  of  large  cities, 
their  light  fluxes  overlap  and  thereby  give  a  better  diffusion,  and, 
at  the  same  time,  the  midway  point  between  lamps  is  under  a 
greater  angle  against  the  horizontal ;  thus  a  more  downward  dis- 
tribution of  the  light  flux  permissible.  For  the  largest  part  of 
American  street  lighting,  however,  this  does  not  apply. 

122.  In  the  early  days  of  using  arc  lamps  for  American  city 
lighting,  lighting  towers  were  frequently  used,  and  such  tower 
lighting  has  still  survived  in  some  cities.  One  or  a  number 
of  arc  lamps  are  installed  on  a  high  tower  and  were  supposed 
from  there,  like  artificial  suns,  to  spread  their  light  over  an  entire 
city  district. 

This  method  of  city  lighting  was  found  unsatisfactory,  as  it 
did  not  give  enough  light.  It  is  unsatisfactory,  however,  not 
in  principle,  but  because  it  was  too  ambitious  a  scheme.  If, 
in  street  illumination,  we  double  the  distance  between  the  lamps, 
each  unit  must  have  four  times  the  light  flux  to  get  the  same 
minimum  flux  density,  as  the  distance  is  doubled,  and  the  flux 
density  decreases  with  the  square  of  the  distance.  At  twice 
the  distance  between  the  lamps,  each  lamp  thus  must  have 
four  times  the  light  flux,  and  each  mile  of  street  thus  requires 
twice  the  power.  Reducing  the  distance  between  lamps  to  one- 
half  reduces  the  power  to  one-half  with  the  same  minimum 
illumination.  In  street  lighting  it  is  therefore  of  advantage  to 
use  as  many  units  of  illuminants  as  possible,  and  bring  them 
together  as  close  as  possible,  and  correspondingly  lower  their 


ILLUMINATION  AND  ILLUMINATING  ENGINEERING.     275 

intensity,  up  to  the  point  where  the  increasing  cost  of  taking 
care  of  the  larger  number  of  units  and  increasing  cost  of  poles 
and  connections  compensates  for  the  decreasing  cost  of  energy. 
There  is  a  minimum  which  probably  is  fairly  near  our  present 
practice. 

When,  however,  you  come  to  square  and  exposition  lighting, 
you  find  that  the  distance  between  the  illuminants  has  no 
effect  on  the  efficiency.  Let  us  assume  that  we  double  the 
distances  between  the  lamps  which  light  up  a  large  area.  Then 
each  lamp  requires  four  times  the  light  flux  to  get  the  same 
minimum  flux  density  between  the  lamps,  but  at  twice  the 
distance  between  the  lamps  each  lamp  illuminates  four  times  the 
area,  and  the  total  power  per  square  mile  of  lighting  a  large  area, 
like  an  exposition,  thus  is  independent  of  the  number  of  lamps 
used,  and,  whether  you  place  them  close  together  or  far  apart, 
you  require  the  same  total  flux  of  light,  and  if  you  keep  the  same 
proportions  of  height  from  the  ground  and  distance  between 
lamps,  you  also  get  the  same  variation  between  maximum  and 
minimum  intensity.  But,  supposing  the  lamps  to  be  placed 
further  apart,  the  maximum  or  minimum  points  also  are  further 
apart,  and  you  get  a  more  satisfactory  illumination  by  having 
a  less  rapid  intensity  variation.  That  points  to  the  conclusion 
that,  for  exposition  lighting,  the  most  efficient  way  would  be  to 
use  a  relatively  moderate  number  of  high-power  sources  of 
light  on  high  towers  at  distances  from  each  other  of  the  same 
magnitude  as  the  height  of  the  towers.  We  would  get  a  greater 
uniformity  and  better  physiological  effect  by  having  the  illumi- 
nants further  apart,  and  they  would  require  the  same  total 
light  flux,  and  therefore  the  same  power,  as  if  you  bring  the  lamps 
close  to  the  ground,  and  place  them  very  close  to  each  other. 
The  tower  lighting  therefore  is  the  ideal  form  for  lighting  a  large 
area.  When  the  arc  was  first  introduced,  it  was  so  much  superior 
to  any  other  illuminant  known  before,  that  people  vastly  over- 
rated it.  They  thought  that  they  could  light  the  whole  city 
by  it,  and  in  trying  to  do  so  these  towers  would  have  been  the 
proper  way,  but  very  soon  it  was  found  that  even  with  the  effi- 
ciency of  the  arc,  to  light  not  only  the  streets,  but  the  whole 
area  of  the  city,  would  require  an  entirely  impracticable  amount 
of  light  flux.  It  thus  was  too  ambitious  a  scheme  for  city 
lighting,  but  it  should  be  done  in  exposition  work.  City  illumi- 


276  RADIATION,  LIGHT,  AND  ILLUMINATION. 

nation  thus  has  come  down  from  this  first  ambition  to  light  the 
whole  city  to  an  attempt  to  light  only  the  streets.  For  the 
latter  purpose,  however,  lighting  towers  are  inefficient,  since 
much  of  the  light  flux  is  wasted  on  those  places  which  we  no 
longer  attempt  to  light.  In  exposition  lighting,  however,  the 
most  effective  general  illumination  would  be  given  by  white 
arcs  on  high  towers,  leaving  the  concentrated  or  decorative 
illumination  to  the  incandescent  lamp  and  flame  arc,  of  yellow 
color. 


LECTURE  XIII. 

PHYSIOLOGICAL  PROBLEMS  OF  ILLUMINATING 
ENGINEERING. 

123.  The  design  of  an  illumination  requires  the  solution  of 
physiological  as  well  as  physical  problems.  Physical  considera- 
tions, for  instance,  are  the  distribution  of  light-flux  intensity 
throughout  the  illuminated  space,  as  related  to  size,  location 
and  number  of  light  sources,  while  the  relation,  to  the  satisfac- 
tory character  of  the  illumination,  of  the  direction  of  the  light, 
its  subdivision  and  diffusion,  etc.,  are  physiological  questions. 
Very  little,  however,  is  known  on  the  latter,  although  the  entire 
field  of  the  physiological  effects  of  the  physical  methods  of 
illumination  is  still  largely  unexplored.  As  result  thereof, 
illuminating  engineering  is  not  yet  an  exact  science,  as  is,  for 
instance,  apparatus  design,  but  much  further  physiological 
investigation  is  needed  to  determine  the  requirements  and 
conditions  of  satisfactory  illumination. 

The  physical  side  of  illuminating  engineering: — to  produce  a 
definite  light  flux  density  throughout  the  illuminated  space, — 
is  ah  engineering  problem,  which  can  be  solved  with  any  desired 
degree  of  exactness,  usually  in  a  number  of  different  ways. 

The  solution  of  the  physical  problem  of  light  distribution, 
however,  does  not  yet  complete  the  problem  of  illuminating 
engineering,  does  not  yet  assure  a  satisfactory  illumination,  but 
with  the  same  distribution  of  light  flux  density  throughout  the 
illuminated  surface,  the  illumination  may  be  anything  between 
entirely  unsatisfactory  and  highly  successful,  depending  on  the  ful- 
fillment or  failure  to  fulfill  numerous  physiological  requirements. 
Some  of  these  are  well  understood  and  such  that  they  can  be 
taken  into  consideration  in  the  physical  design  of  the  illumina- 
tion, and  thus  no  excuse  exists  to  fail  in  their  fulfillment,  though 
it  is  frequently  done.  Such,  for  instance,  is  the  requirement  of 
low  intrinsic  brilliancy  in  the  field  of  vision,  of  the  color  of  the 
light,  etc.  Other  physiological  requirements  are  still  very  little 

277 


278  RADIATION,  LIGHT,  AND  ILLUMINATION. 

understood  or  entirely  unknown,  while  on  others  not  sufficient 
quantitative  data  are  available  for  exact  engineering  calculation. 

Thus,  for  instance,  the  usual  suburban  street  illumination, 
with  arcs  spaced  at  considerable  distances  from  each  other  and 
located  on  fairly  low  posts,  is  very  much  inferior  to  the  illumina- 
tion given  by  moonlight,  even  when  allowing  for  the  difference 
in  intensity.  Here  the  reason  of  the  unsatisfactory  character 
of  the  former  illumination  is  mainly  the  almost  horizontal  direc- 
tion of  the  light  flux.  A  perfectly  vertical  direction  of  the  light 
flux  again  is  unsatisfactory  in  many  cases,  and  the  most  satis- 
factory results  are  given  by  a  direction  of  the  light  flux  which 
makes  a  considerable  angle  with  the  horizontal  as  well  as  the 
vertical  direction.  Thus,  when  dealing  with  directed  light,  the 
direction  angle  is  of  essential  physiological  importance.  We 
have  very  little  exact  knowledge  to  guide  in  the  determination 
of  the  proper  angle  in  which  to  direct  the  light  flux ;  it  is  known 
that  in  general  approximately  horizontal  and  approximately 
vertical  direction  of  the  light  flux  are  objectionable,  and  an  in- 
termediary angle  gives  best  results.  However,  the  horizontal 
direction  usually  is  objectionable  by  excessive  contrasts,  the 
vertical  direction  by  flatness  in  the  appearance  of  the  illuminated 
objects,  and,  depending  on  the  nature  of  the  objects,  sometimes 
the  one,  sometimes  the  other  feature  may  be  more  objectionable. 
Hence,  the  best  angle  of  incidence  of  the  light  depends  on  the 
nature,  that  is,  the  shape  and  location,  of  the  illuminated  objects, 
on  the  purpose  of  the  illumination,  etc.,  and  thus  is  not  con- 
stant, but  is  a  function  of  the  problem,  which  is  still  largely 
unknown. 

124.  Not  represented  by  the  physical  distribution  curve  of 
illumination,  but  very  marked  in  their  physiological  effect  is 
the  difference  between  directed  light  and  diffused  light.  In  most 
problems  of  illumination,  either  entirely  directed  light  or  entirely 
diffused  light  is  unsatisfactory,  and  a  combination  of  directed 
light  and  diffused  light  is  required,  as  discussed  in  the  preceding 
pages.  No  exact  knowledge,  however,  exists  on  the  proportion 
in  which  directed  light  and  diffused  light  should  be  combined 
for  satisfactory  illumination,  nor  how  this  proportion  varies  with 
the  nature,  color,  etc.,  of  surrounding  objects,  with  the  purpose 
of  the  illumination,  etc.  That  it  varies  is  well  known,  as  for 
some  purposes,  as  a  draughting  room,  entirely  diffused  light 


PHYSIOLOGICAL  PROBLEMS.  279 

seems  best  suited,  while  for  other  purposes  mainly  directed  light 
seems  more  satisfactory. 

Furthermore,  the  relations  between  directed  and  diffused  light 
have  in  the  illuminating  engineering  practice  been  obscured  to 
some  extent  by  the  relation  between  high  and  low  intrinsic  bril- 
liancy and  between  direct  and  indirect  lighting.  Thus,  to 
eliminate  the  objectionable  feature  of  high  intrinsic  brilliancy  of 
the  illuminant,  direct  lighting  by  light  sources  of  high  brilliancy, 
which  was  largely  directed  lighting,  has  been  replaced  by  indirect 
lighting,  by  reflection  from  ceilings,  etc.,  which  is  diffused  light- 
ing. Where  such  change  has  resulted  in  a  great  improvement  of 
the  illumination,  it  frequently  has  been  attributed  to  the  change 
from  directed  to  diffused  lighting,  while  in  reality  the  improve- 
ment may  have  been  due  to  the  elimination  of  high  brilliancy 
light  sources  from  the  field  of  vision,  and  engineers  thereby  led 
to  the  mistaken  conclusion  that  perfectly  diffused  lighting  is  the 
preferable  form.  Again,  in  other  instances  such  a  change  from 
direct  to  indirect  lighting  has  not  resulted  in  the  expected  im- 
provement, but  the  indirect  lighting  been  found  physiologically 
unsatisfactory,  and  the  conclusion  drawn  that  the  elimination 
qf  high  brilliancy  from  the  field  of  vision  has  not  been  beneficial, 
while  in  reality  the  dissatisfaction  with  the  indirect  light  was  due 
to  the  excess  of  diffused  light  and  absence  of  directed  light,  and 
this  improper  proportion  between  directed  and  diffused  light 
more  than  lost  the  advantage  gained  by  eliminating  the  light 
sources  of  high  brilliancy  from  the  field  of  vision.  In  this  case 
the  proper  arrangement  would  have  been  to  reduce  the  brilliancy 
of  the  light  sources,  by  diffusing  or  diffracting  globes,  to  a  suffi- 
ciently low  value,  but  leave  them  in  such  position  as  to  give  the 
necessary  directed  light. 

Thus,  in  illuminating  engineering,  as  in  other  sciences,  it  is 
very  easy  to  draw  erroneous  conclusions  from  experience  by 
attributing  the  results  to  a  wrong  cause.  Any  change  in  the 
arrangement  usually  involves  other  changes:  as  in  the  above 
instance,  the  change  from  high  to  low  brilliancy  commonly 
causes  a  change  from  directed  to  diffused  light;  by  attributing 
the  results  to  a  wrong  cause,  serious  mistakes  thus  may  be  made 
in  basing  further  work  on  the  results. 

125.  In  discussing  diffused  light,  we  must  realize  that  the 
meaning  of  " diffused  light"  is  to  some  extent  indefinite.  To 


280 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


define  diffused  light  as  light  which  traverses  the  space  in  all  direc- 
tions and  thus  casts  no  shadow,  is  not  correct,  since  even  diffused 
daylight  casts  shadows.  For  instance,  if  in  Fig.  122  P  is  the  sur- 


M/w///^^^^^ 

FIG.  122. 

face  of  the  ground  and  A  a  flat  circular  shade  at  distance  I  above 
the  ground,  the  intensity  distribution  of  the  light  in  plane  P  is  as 
shown  in  Fig.  122  for  I  =  0.2  A,  thus  showing  a  fairly  dark 
shadow  beneath  the  center  of  A,  but  a  shadow  which  blurs  so 
very  gradually  that  with  most  objects  it  is  not  marked. 

The  light  from  a  single  point  source 
is  perfectly  directed  light;  it  traverses 
every  point  of  space  in  one  single 
direction  only,  as  shown  as  A  in  Fig. 
123.  If  we  now  enclose  the  point 
source  in  an  opal  globe,  which  then 
becomes  the  radiator,  as  discussed 
before,  as  diagrammatically  shown  as 
B  in  Fig.  123,  the  light  flux  traverses 
each  point  not  in  a  single  direction  but 
in  all  directions  within  a  narrow  angle 
a,  which  is  the  angle  subtended  by 
the  radiator  L  from  the  point  P. 
With  increasing  size  of  the  illuminant, 
and  thus  increasing  angle  a,  C,  Fig. 
123,  the  pencil  of  rays,  which  traverses 
point  P,  gradually  spreads,  until,  when 
a  becomes  180  deg.,  we  get  perfectly 
diffused  light,  similar  to  daylight. 
Hence,  with  a  gradual  change  of  the  diameter  of  the  illum- 
inant, from  a  =  0  to  a.  =  180  deg.,  the  light  gradually  changes 
from  directed  to  diffused  light.  Thus,  no  sharp  dividing  line 


FIG.  123. 


PHYSIOLOGICAL  PROBLEMS.  281 

can  be  drawn  between  directed  light,  and  diffused  light,  but 
the  directed  light  from  a  light  source  of  considerable  diameter 
(that  is,  a  diameter  which  is  not  neglible  compared  with  the  dis- 
tance of  the  illuminated  objects  from  the  light)  already  has  to 
some  extent  the  character  of  diffused  light. 

Diffused  light  thus  may  be  denned  as  light  given  by  a  radiator 
which  subtends  a  spherical  angle  equal  to  a  considerable  part  of 
the  sphere.  This  makes  the  term  "diffused  light"  a  relative 
term.  Near  to  a  radiator  of  considerable  size,  the  light  given 
by  this  radiator  thus  is  largely  diffused  light,  while  at  considerable 
distance  it  is  practically  directed  light,  or,  in  other  words,  the 
light  given  by  light  sources  of  considerable  size  is  directed  light 
only  at  such  distances  from  the  radiator  at  which  the  law  of 
inverse  squares  holds;  but  approaching  the  radiator  so  far 
that  this  law  of  inverse  squares  (flux  density  inverse  proportional 
to  the  square  of  the  distance)  does  not  hold,  the  light  approaches 
somewhat  the  character  of  diffused  light. 

The  physiological  effects,  however,  during  a  gradual  change 
from  a  =  0,  or  directed  light,  to  a  =  180  deg. ,  or  diffused  light, 
apparently  do  not  change  uniformly,  but  new  effects  appear 
and  others  disappear. 

126.  The  main  objection  to  directed  light  from  a  single  source 
results  from  the  absence  of  light  in  the  shadows.  Using,  how- 
ever, two  or  more  illuminants,  that  is,  combining  directed  light 
of  several  widely  different  directions,  the  shadow  cast  by  one 
illuminant  is  illuminated  by  the  other  illuminants,  and  thus  an 
effect  produced  very  similar  to  diffusion.  Thus  with  two  light 
sources,  at  a  point  at  which  both  light  sources  give  the  same 
illumination,  the  intensity  in  the  shadow  cast  by  one  illuminant 
is  still  50  per  cent,  that  is,  the  illumination  the  same  as  if  equal 
volumes  of  directed  and  of  diffused  light  were  combined,  and 
to  a  considerable  extent  the  physiological  effect  is  the  same. 
It  is  not  completely  so,  however.  In  the  illumination  by  equal 
volumes  of  diffused  light  and  directed  light  from  a  single  source, 
each  object  casts  a  single  shadow,  in  which  the  illumination  is 
reduced  to  half.  When  producing  an  equivalent  diffusion  by 
two  light  sources,  an  object  casts  two  shadows,  in  which  the 
illumination  is  reduced  to  half  (if  the  two  light  sources  give 
equal  illumination),  but,  where  the  shadows  overlap,  a  perfectly 
black  and  lightless  shadow  is  produced.  The  more  the  two 


282          RADIATION,  LIGHT,  AND  ILLUMINATION. 

half  shadows  overlap  to  a  complete  shadow,  the  less  the  combina- 
tion of  the  two  light  sources  is  equivalent  to  diffusion.  At 
the  same  time,  occasionally  the  existence  of  two  or  more  half 
shadows  and  of  their  compound  shadows  may  assist  distinction, 
and  thereby  be  advantageous.  In  short,  there  is  a  vast  and 
largely  unexplored  field  in  the  physiology  of  illumination, 
which  the  illuminating  engineer  will  have  to  study  and  investi- 
gate. 

While  one  point  source  of  light  gives  directed  light,  two 
sources  at  distances  from  each  other  give  an  effect  equivalent 
to  diffusion,  and  three  or  more  sources  still  more  so,  until  in  the 
theoretical  case  of  an  infinite  number  of  point  sources  distributed 
through  space  — or,  practically,  a  very  large  number  of  distrib- 
buted  illuminants  — we  get  perfect  diffusion.  With  a  change 
from  a  single  to  a  very  large  number  of  illuminants,  the  illumi- 
nation thus  changes  from  directed  to  diffused,  and  thus,  for 
a  moderate  number  of  illuminants,  is  intermediate  between 
directed  and  diffused,  but  nevertheless  this  intermediate  state  is 
physiologically  of  entirely  different  character  from  that  given 
by  a  single  illuminant  of  very  large  diameter,  that  is  large 
angle  a,  as  discussed  above. 

127.  We  thus  have  true  diffused  light,  as  daylight,  the  equiva- 
lent diffusion  given  by  the  combination  of  several  light  sources, 
which  depends  on  their  relative  location,  and  the  equivalent 
diffusion  given  by  a  large  relative  diameter  of  the  light  source. 
The  latter  again  varies  with  the  shape  of  the  light  source,  and 
in  extreme  cases,  as  a  linear  straight  radiator,  as  a  Geissler  tube 
(Moore  tube),  we  may  get  an  illumination  which,  at  any  point 
of  space,  is  practically  diffused  in  one  direction,  and  practically 
directed  in  a  direction  at  right  angle  to  the  former.  In  such 
cases  we  again  get  different  physiological  phenomena.  For 
instance,  a  straight  rod,  held  parallel  to  the  radiator,  casts  a 
sharp  black  shadow  —  directed  light  —  while,  when  held  at  right 
angles  to  the  radiator,  it  casts  no  shadow  —  diffused  light.  With 
objects  of  more  irregular  shape,  it  can  be  seen  that  the  shape 
and  appearance  of  the  shadows  give  a  rather  interesting  problem, 
and  the  physiological  impression  made  by  such  illumination 
thus  is  different  again,  from  that  of  ordinary  directed  or  diffused 
light  or  their  combination. 

In  general,  wherever  two  or  more  illuminants  are  used,  the 


PHYSIOLOGICAL  PROBLEMS.  283 

physiological  effect  depends  on  the  relative  position  of  the  light 
sources  to  the  illuminated  objects,  irrespective  of  the  intensity  of 
illumination.  Thus,  for  instance,  in  the  illumination  shown  in 
Fig.  117,  on  the  same  curve  of  equal  illumination,  the  physiologi- 
cal effect  is  not  constant,  but  varies  from  point  to  point.  On  the 
curve  of  850  near  the  center  of  the  room,  an  object  casts  four 
shadows  of  approximately  equal  intensity,  in  different  direc- 
tions. The  shadows  are  sufficiently  marked  to  assist  in  seeing, 
and  the  illumination  in  the  shadow  is  quite  high ;  thus  the  illumi- 
nation is  very  satisfactory.  On  the  same  curve  850,  near  the 
edge  of  the  room,  the  four  shadows  fall  in  nearly  the  same 
direction,  only  one  is  marked,  and  by  the  overlap  of  the  shadows 
a  large  compound  shadow  is  formed,  in  which  the  illumination 
is  very  low,  distinction  difficult,  and  the  illumination  thus 
unsatisfactory.  Thus  with  the  same  physical  value  of  illumina- 
tion, on  the  same  curve  850,  the  physiological  effect  in  this  case 
changes  from  a  very  satisfactory  illumination  at  one  place, 
to  a  quite  unsatisfactory  illumination  at  another  place.  Thus, 
in  this  instance,  while  the  solution  of  the  illuminating  problem, 
given  in  Fig.  117,  is  physically  perfect,  that  is,  the  illumination 
very  uniform  throughout  the  entire  room,  and  the  efficiency 
high,  physiologically  the  illumination  is  satisfactory  only  in 
the  middle  of  the  room,  but  becomes  more  and  more  unsatisfac- 
tory the  further  we  go  outside  of  the  square  formed  by  the  four 
light  sources.  Physiologically  the  illumination  would  probably 
be  improved  by  locating  the  light  sources  in  the  four  corners 
of  the  ceiling,  or  in  the  centers  of  the  four  sides  of  the  ceiling. 
Physically,  this  arrangement  of  lamps  in  the  corners  of  the  room 
would  greatly  reduce  the  efficiency,  thus  require  either  more 
power,  or  lower  the  average  illumination;  the  arrangement  of 
the  lamps  at  the  sides  would  decrease  the  efficiency  less,  but 
would  considerably  impair  the  uniformity  of  illumination,  giving 
a  lower  illumination  near  the  corners  of  the  room. 

Furthermore,  in  illuminating  engineering,  enters  as  an  impor- 
tant and  largely  unknown  factor,  the  effect  on  the  physical  and 
physiological  illumination,  of  the  objects  in  the  illuminated 
space,  and  of  the  observer]  that  is,  the  light  flux  distribution 
and  its  physiological  effect,  as  depending  on  the  location  of 
light  sources  and  distribution  of  their  light  flux  through  the 
illuminated  space,  is  not  sufficient  to  solve  the  problem  of 


284          RADIATION,  LIGHT,  AND  ILLUMINATION. 

illumination,  but  consideration  must  be  given  to  the  changes 
resulting  from  the  use  of  the  illumination.  For  instance,  in 
the  illumination  shown  in  Fig.  117,  and  discussed  above,  the 
diffused  light,  0.250,  resulting  from  reflection  from  walls  and 
ceiling,  is  quite  considerable,  and  would  be  nearly  sufficient 
for  giving  distinction  in  the  compound  shadow  of  all  four  illumi- 
nants,  as  it  exists  in  a  pronounced  degree  near  the  walls.  Thus 
even  there  the  illumination  would  be  moderately  fair.  How- 
ever, when  relying  on  this  diffused  illumination  to  see  in  the 
shadow  of  objects  close  to  the  walls,  it  may  not  be  present,  or 
largely  reduced  by  the  shadow  of  the  observer,  since,  as  seen 
above,  diffused  light  also  casts  shadows,  though  the  blur  at 
the  edges  of  these  shadows  is  such  as  to  make  them  very  little 
noticeable.  Thus,  when  approaching  close  to  the  walls  to  look 
at  an  object,  we  may  find  it  shaded  from  the  direct  light  and 
from  most  of  the  diffused  light,  thus  giving  unsatisfactory 
illumination.  Locating  the  light  sources  in  the  corners  or  the 
centers  of  the  sides  of  the  room,  we  get  pronounced  shadows 
of  the  objects  located  against  the  walls  of  the  room,  and  thereby 
again  unsatisfactory  illumination,  although  in  this  case,  physio- 
logically, considering  merely  the  room  without  the  objects  which 
may  be  located  in  it,  the  illumination  would  be  satisfactory. 
Thus  we  may  have  to  sacrifice  uniformity  of  illumination  still 
further,  by  arranging  five  light  sources,  four  in  the  corners 
of  centers  of  the  sides  of  the  room,  and  one,  of  larger  light  flux, 
in  the  center  of  the  ceiling. 

Thus,  occasionally,  illuminations  designed  for  uniform  flux 
density  are  not  satisfactory,  even  though  the  proportion  of 
directed  and  of  diffused  light,  and  the  direction  of  the  directed 
light,  is  physiologically  correct,  because  the  changes  resulting 
from  the  objects  in  the  room,  and  the  person  of  the  user  of  the 
illumination,  are  not  sufficiently  considered. 

129.  The  cause  of  most  of  these  difficulties  in  dealing  with 
illuminating  problems  is  that,  physiologically,  light  is  not  a 
vector  quantity;  that  is,  light  flux  densities  cannot  be  combined 
by  the  parallelogram  law. 

Two  magnetomotive  forces  A  and  B,  Fig.  124,  acting  on  the 
same  point  P,  combine  by  the  parallelogram  law  to  a  resultant 
C;  that  is,  the  combined  action  of  A  and  B  is  identical  with  the 
action  of  a  single  m.m.f.  C.  Thus  the  m.m.f.  existing  at  any 


PHYSIOLOGICAL  PROBLEMS. 


285 


point  P  of  space  is  perfectly  characterized  by  two  quantities 
only  —  the  resultant  intensity,  C,  and  its  direction. 

If,  however,  in  Fig.  125,  A  and  B  represent  the  two  light 
flux  densities  produced  at  point  P  by  two  light  sources  I/t 
and  L2,  their  physiological  and  also  their  physical  action  may 
be  entirely  different  from  that  of  one  light  flux  C  derived  by 
combining  A  and  B  by  the  parallelogram  law. 


FIG.  124. 


FIG.  125. 


In  some  respects  the  action  of  the  two  separate  flux  densities 
A  and  B  is  the  same,  or  nearly  the  same,  as  that  of  a  resultant 
flux  density  C;  the  illumination  of  an  opaque  plane  a,  located 
so  that  both  light  sources  Ll  and  L2  are  on  the  same  side  of  the 
plane,  is  the  same.  If,  however,  the  illuminated  plane  is  trans- 
parent or  translucent,  and  also  in  regard  to  the  effects  of  polariza- 
tion, reflection  etc.,  the  effect  of  the  two  separate  flux  densities 
A  and  B  differs  from  that  of  a  single  resultant  C.  Entirely 
different  is  the  effect  if  the  light  sources  Lt  and  L2  are  on  dif- 
ferent sides  of  the  plane.  Thus,  with  a  plane  c  located  in  the 
direction  C,  the  resultant  flux  density  C  would  give  no  illumina- 
tion, while  in  reality  by  A  and  B  both  sides  of  the  plane  are 
fairly  well  illuminated.  Thus,  with  the  plane  in  any  direction 
within  the  angle  cu  between  PL2  and  PA,  it  receives  the  same 
amount  of  light  from  A  and  B  as  it  would  receive  from  (7;  but 
in  any  direction  within  the  angle  T  =  7t  —  to,  between  PA  and 
PB,  it  receives  more  light  from  A  and  B  than  it  would  receive 


286 


RADIATION,  LIGHT,  AND  ILLUMINATION. 


from  the  resultant  C,  and  receives  infinitely  more  light  in  the 
direction  c  (that  is,  in  this  direction  it  receives  no  light  from  C). 
Within  this  angle  T,  both  sides  of  the  plane  are  illuminated 
by  A  and  B,  which  obviously  is  never  possible  by  a  resultant 
vector  C. 

In  the  illumination  of  a  plane,  the  differences  between  the  ac- 
tual illumination  by  A  and  B  and  the  illumination  which  would 
result,  if  light  were  a  vector  quantity,  by  (7,  are  only  those  of 
intensity  of  illumination.  With  an  object  of  different  shape, 
however,  the  phenomenon  becomes  far  more  complex.  Thus  the 
illumination  of  a  sphere  S  by  the  resultant  C  would  be  as  shown 
in  Fig.  126,  — half  the  sphere  dark,  the  other  half  light,  and  with 
a  maximum  intensity  at  c,  shading  off  towards  zero  at  the  termi- 
nator mn.  The  actual  illumination  as  shown  in  Fig.  127  gives  a 


FIG.  126. 


FIG.  127. 


black  segment  of  angle  <D,  while  more  than  half  the  circumference 
of  the  sphere  is  illuminated.  The  maximum  intensity  is  at  the 
same  place  c,  and  of  the  same  intensity  as  in  Fig.  123  but 
the  total  light  flux  received  by  the  sphere  is  far  greater  than 
would  be  received  from  the  resultant  C,  and  is  the  sum  of  the 
light  fluxes  received  from  the  two  light  sources.  Thus : 

In  the  illumination  of  a  sphere  the  light  flux  densities  are 
added,  irrespective  of  their  direction,  and  not  vectorially  com- 
bined. 

In  the  illumination  of  a  plane,  by  light  sources  which  all  lie 
on  the  same  side  of  the  plane,  the  light  flux  densities  are  vectori- 
ally combined. 


PHYSIOLOGICAL  PROBLEMS,  287 

With  other  shapes  of  objects,  the  total  received  light  flux  may 
even  be  more  than  corresponds  to  the  sum  of  the  component  flux 
densities. 

As  in  general  illumination  for  distinguishing  objects  we  have 
to  deal  with  all  possible  shapes,  it  thus  follows  that  for  the  gen- 
eral problem  of  illumination  the  resultant  effect  is  most  nearly 
related  to  the  "total  flux  density"  or  "total  illumination"  as 
derived  by  adding,  irrespective  of  their  direction,  all  the  light 
flux  densities,  as  was  done  in  the  preceding  lectures  when  dealing 
with  light  flux  distribution.  Only  in  special  cases,  as  the  illumi- 
nation of  a  draughting  table,  the  flux  density  in  one  particular 
direction  is  of  importance,  and  was  used  as  the  "  horizontal  illu- 
mination" in  the  instance  represented  by  Figs.  119  to  121. 

130.  While  the  resultant  effect,  or  the  total  illumination,  is  de- 
rived by  adding  the  flux  densities  irrespective  of  their  direction, 
in  the  physiological  effect,  that  is,  the  appearance,  the  direction 
plays  an  essential  part.  Thus  a  sphere  located  as  in  Fig.  127 
looks  different  than  it  looks  in  Fig.  126,  even  if  it  receives  the 
same  total  light  flux.  Still  more  marked  is  this  difference  with 
more  complex  shapes  of  the  illuminated  objects.  Thus  a  land- 
scape looks  different  with  every  different  position  of  the  sun  in 
the  sky,  and  different  again  in  the  diffused  light  of  a  cloudy  day, 
irrespective  of  the  intensity  of  the  illumination.  Under  some 
conditions  sharp  contrasts  appear,  where  under  other  illumina- 
tions the  appearance  is  flat,  and  with  the  change  of  illumination 
contrasts  disappear  in  some  places,  appear  in  others,  etc.;  that 
is,  the  appearance  of  a  complex  body  very  greatly  varies  with 
the  character  of  the  illumination,  entirely  independent  of  its 
intensity. 

With  artificial  illumination  it  then  is  the  problem  of  the 
illuminating  engineer  to  design  the  illumination  so  as  to  bring 
out  contrasts  where  required  by  the  purpose  of  the  illumination, 
reduce  them  where  too  great  or  unnecessary,  etc.  If  we  consider 
the  possible  personal  equations  of  the  user  of  the  illumination 
as  depending  on  his  physical  nature,  occupation  or  state,  further- 
more the  effect  of  the  color  of  light  and  the  marked  physiological 
effect  which  even  slight  variations  in  the  color  shade  produce,  it 
can  be  seen  that  the  success  of  illuminating  engineering  prob- 
lems still  largely  depends  on  the  judgment  of  the  designer,  and 
this  judgment  is  not  yet  guided  by  any  extended  exact  experi- 


288  RADIATION,  LIGHT,  AND  ILLUMINATION. 

ence,  thus  rather  uncertain.  An  enormous  amount  of  work  is 
still  to  be  done  mainly  in  the  field  of  "engineering  physiology/7 
before  the  design  of  a  system  of  illumination  can  approach  the 
same  exactness  as  for  instance  the  design  of  long-distance  trans- 
mission or  other  engineering  work. 


INDEX. 


PAGE 

Absolute  color  in  illumination 265 

Absorption  of  excess  of  light  flux 261 

of  light  by  body 28 

spectrum 27 

Acclimatization  to  radiation 59 

Acetylene  flame 130 

standard 178 

Acoustic  scale  of  frequency 14 

Actual  or  objective  color 33 

Adaptability  range  of  eye 38 

Albedo  of  ceiling 246 

radiator 85 

reflector 212, 215 

walls 246 

whiteness 30 

Allotropic  modifications  of  carbon 81 

Alternating  arc 114,  116,  125 

Alternating  current  field,  frequency  and  wave  length 17 

as  polarized  wave 8 

Amyl  acetate  lamp 177 

Analytic  action  of  animal  organism 65 

Angle  of  directed  light 278 

Angstrom  unit 7 

Animal  organism,  analytic  action 65 

Apparent  or  subjective  color 34 

Arc  characteristics 138 

conduction 105 

conductor 105, 110 

electric 98 

efficiency  of  light  production 122 

flame 110 

Arcing  ground,  frequency  and  wave  length 17 

Arc  lamps 151 

photometry 182 

rectifier 114 

spectrum 105 

stability  curve 144 

stream 105 

street  illumination 234 

as  unidirectional  conductor 113 

289 


290  INDEX. 

PAGE 

Arc  voltage  curve 139 

Area  lighting 275 

Armature  reaction  of  arc  machine 163 

Artificial  illumination,  domestic  lighting 271 

more  harmful  than  daylight 54 

Auxiliary  arc  starting  main  arc 112 

Band  spectrum 26 

Base  filament 81 

Beam  of  searchlight,  intensity 234 

Biological  phosphorescence 96 

Black 32 

body 29 

radiation 84,  88 

of  hydrocarbon  flame ,  134 

Blood,  opaque  for  ultra-violet  light 58 

transparent  for  long  light  waves 58 

Blue  light,  specific  effect 51 

Blurring  of  the  shadow  in  illumination 268 

vision 54 

Borides  as  refractory  bodies , 78 

Bolometer  measuring  radiation  power 166 

Brightness  of  walls  and  ceiling  in  domestic  lighting 270 

Brilliancy  and  contraction  of  pupil 262 

of  light  sources 256,  259 

objectionable  effect 263 

of  radiator 189,  221 

Brush  arc  machine 163 

Brush  discharge 101 

Bunsen  photometer 170 

Burns  by  radiation 48 

Calcium  arc,  orange  yellow 123 

carbide  arc 124 

Calculation  of  room  illumination 247 

street  illumination 238 

Candle 128 

power 186 

equivalent 258 

standard  of  light 177 

unit  of  light  intensity 257 

Carbides  as  refractory  bodies 78 

Carbon,  allotropic  modifications 81 

arc 140 

distribution 203 

efficiency 122 

electrode  as  radiator 190,  193 


INDEX.  291 

PAGE 

Carbon,  arc,  incomplete  rectification 117 

lamp  as  incandescent  radiator 76 

not  a  typical  arc 109 

in  street  illumination 236,  240 

bisulphide  lamp 135 

filament  as  radiator 195 

as  refractory  element 77 

vapor  tension 79 

Cathode  of  arc 108 

Ceiling,  albedo 246 

Change  carbons 82 

Characteristics  of  the  arc 137 

Chemical  action  of  light 63 

on  plants 64 

luminescence 97 

of  flame 133 

phosphorescence 95 

rays 63 

Chimney  of  luminous  arc  lamp 158 

Chlorophyl 64 

Circular  cylinder  as  radiator 197 

line  as  radiator 197 

plane  as  radiator 190 

shading  circular  radiator 203 

shading  linear  radiator 210 

radiator  shaded  by  circular  plane 203 

Circulating  flame  lamp 126 

Clutch  of  arc  lamp 153 

Cold  light 48 

Color  change  of  light  of  arc 118 

differences  in  illumination 265 

photometry 172 

Colored 33 

body 29,  31,  36 

lights,  comparison 42 

radiation 85 

radiator  of  magnesium  flame 134 

Color  effect  in  illuminating  engineering 269 

street  lighting 272 

Colorless 32 

body 29,  31,  36 

Color  of  light  and  economy 269 

fatigue 265 

Combination  of  light  fluxes  by  addition 285 

Comfort  and  economy  in  domestic  lighting 270 

Comparison  of  arcs  for  street  lighting 236 

colored  light 42 


292  INDEX. 

PAGE 

Comparison  of  globes  regarding  light  flux  distribution 224 

illumination  curves 232 

radiators 202 

and  shadows 209 

reflectors 215 

Concentrated  illumination 260 

or  local  illumination 269 

Conduction,  continuous 98, 105 

disruptive 98 

Constant  current  system  of  arc  lighting 162 

Constructive  action  of  plant 65 

Continuous  conduction 98, 105 

spectrum 26 

Continuity  of  the  arc  at  the  cathode Ill 

Contraction  of  pupil 38,  262 

Control  of  subjective  color  in  illumination 265 

Core  of  arc  flame 110 

Corona 101 

Crater  of  the  arc  as  radiator 191 

Crookes'  radiometer 10 

Cylindrical  radiator 195 

Daylight  illumination,  domestic  lighting 271 

Defects  of  street  lighting 273 

Density  of  light  flux , 256, 259 

Destructive  effect  of  radiation 48,  57,  59 

short  ultra-violet  light 52 

Dielectric  constant  and  refractive  index 24 

Differences  of  color  in  illumination 265 

intensity  in  illumination 265 

Differential  arc  lamp 156 

Diffracting  globe  and  light  flux  distribution 223 

Diffraction  grating 26 

and  light  distribution 221 

spectroscope 26 

Diffused  and  directed  light 267,  269 

illumination 251,  266 

in  indoor  lighting 246 

light,  definition 279 

and  directed  light,  proportions 278 

shadow 280 

Diffusing  globe  and  light  flux  distribution 223 

Diffusion,  equivalent 281 

and  light  distribution 221 

by  number  of  radiators 281 

by  size  of  radiator 280 

Directed  and  diffused  light 267,  269 


INDEX.  293 

PAGE 

Directed  light  266 

angle  of  direction. .  .  .• 278 

Direct  and  indirect  illumination 269 

Discontinuity  of  the  arc  at  the  anode 112 

Disease  germs,  action  of  light 61 

Disinfecting  action  of  light 60 

Disruptive  conduction 98 

voltage 99 

and  gas  pressure 100 

Distinction  between  arc  and  Geissler  discharge 106 

of  objects  by  shadow .' 267 

Distributed  and  massed  illumination 269 

Distribution  curve  and  design  of  incandescent  lamp 243 

of  frosted  globe 221 

of  light 180,  187,  256 

of  opal  globe v 221 

in  street  lighting 272 

Domestic  lighting 226,  270 

Double  refraction 9 

Downward  candle  power 184 

Ear  as  analytic  organ 21 

Economies  of  flame  arc  lamp 212 

Efficiency  and  arc  length 146 

of  illuminant 186 

light  production  by  arc 118,  122 

light  production  by  incandescence 74,  81 

room  illumination 253 

Electric  waves,  engineering  importance 18 

frequency 15 

Electro-conduction  feeding  arc 123 

Electro-luminescence,  efficiency 126 

of  gases  and  vapors 98 

solids 95 

Ellipse,  circumference 198 

Emulsions  as  translucent  bodies 32 

Enclosed  arc  efficiency 148 

carbon  arc 160 

in  street  lighting 236 

Energy  of  plant  life  derived  from  radiation 65 

Engineering  physiology 288 

Equatorial  distribution  of  light 181 

Equiluminous  curves 251 

Equivalent  candle  power 258 

diffusion 281 

Etched  glass  globe,  diffraction 221 

Ether. .                                       7 


294  INDEX. 


Ether  as  carrier  of  energy 7 

form  of  matter 7 

Euler's  theory  of  radiation 4 

Evaporation  of  carbon 79 

Exposition  lighting 275 

Eye  perceiving  only  the  resultant 21 

structure  of 37 

Fatigue  and  color  of  light 265 

of  the  eye 263 

optic  nerve 38 

Fechner's  law 39 

Feeding  device  of  arc  lamp 151 

Filament,  single  loop,  distribution  curve 199 

Fire-fly,  light  of 96 

Fireworks 98 

Fixed  arc  length  of  luminous  arc 158 

Flame  arc  distribution 212 

Flame  carbon  arc 123,  160 

distribution 212 

Flames  as  illuminants 128 

Flicker  photometer. 173 

Flickering  of  the  arc 110 

Floating  system  of  arc  control 156 

Fluorescence 66,  94 

spectrum ! 27,  69 

Fluorescent  bodies 30 

Flux  of  light -256,  259 

Frequency  converter  of  radiation 13,  31 

of  radiation 7 

and  temperature 73 

scale  of  acoustic 14 

of  ultra-violet  radiation 14 

Frosted  globe 262 

diffraction 221 

Gas  flame 128 

pressure  and  disruptive  voltage 100 

Gasolene  deposited  carbon 81 

flame 128 

Geissler  discharge 98 

tube  efficiency 104 

glow 100 

lighting 104 

General  illumination 260 

or  uniform  illumination 269 

German  candle 178 


INDEX.  295 

PAGE 

Germicidal  action  of  light 60 

Glass,  opaque  for  ultra-violet  light 13 

as  protection  against  ultra-violet  light 55 

Globes,  comparison  of  light  distribution 224 

Glow  of  Geissler  tube 100 

Grey  body 30 

radiation 84,  93 

Gypsum,  transparent  for  ultra-violet  light 13 

Harmful  effect  of  light  on  vegetation 56 

radiation 48 

violet  and  ultra-violet 52 

Harmless  radiation 48 

Harmlessness  of  artificial  illuminants 56 

Harmonics  of  radiation 20 

Heat  evaporation  feeding  arc 123 

Heat  evaporation  from  positive  terminal  of  arc 109 

luminescence 91,  93,  96 

at  positive  terminal  of  arc 109 

radiation 1 

rays 63 

Hefner  lamp 178 

Helium 78 

Hemispherical  candle  power 185 

Hertzian  waves,  frequency  and  wave  length 16,  17 

High  frequency  currents,  frequency  and  wave  length 17 

light,  therapeutic  action 61 

Hollow  circular  surface  as  radiator 191 

Holophane  globe 262 

Horizontal  candle  power  of  incandescent  lamp 258 

illumination 226,  287 

of  room 253 

intensity 184 

of  light 182 

table  illumination 253 

Hydrocarbon  flames 128 

Hydro-oxygen  flame 136 

Iceland  spar 9 

Illuminant 256 

Illuminating  engineering 256 

Illumination 177,  179,  256,  259 

Illumination  curves 226,  229 

of  arcs  for  street  lighting 236 

comparison 232 

of  incandescent  lamp 244 

of  table  by  incandescent  lamps 254 


296  INDEX. 

PAGE 

Illumination,  horizontal 226 

objective 261 

problems 260 

of  streets  by  arcs 234 

subjective 262 

of  table  by  incandescent  lamp 253 

total 226 

uniform 226 

vertical 227 

Illuminometer  in  indoor  illumination 253 

Imperfectly  transparent  bodies 31 

Incandescent  lamp 76 

design  and  distribution  curve 243 

illumination 242 

photometry 182 

Indirect  and  direct  illumination 269 

lighting 262 

Indoor  illumination,  calculation 247 

by  incandescent  lamps 242 

Inflammation  of  the  eye  by  ultra-violet  light 53 

radiation 48 

Infra-red  rays 12 

Integrating  photometry 183 

sphere  and  photometry 184 

Intensity  curves  of  arcs  for  street  lighting 256 

comparison 232 

comparison  of  radiators 197 

differences  in  illumination 265 

of  light 257 

of  light  source 256,  259 

Interference , 6 

rings 6 

Intermediary  color  in  photometry 172 

Intermediate  carbon 83 

International  candle 178 

Intrinsic  brilliancy,  see  Brilliancy. 

Iridescence 6 

Iron  arc 119 

giving  ultra-violet  light 13 

Irregular  reflection 28 

and  light  distribution 212 

Irritation  by  uniform  intensity  of  illumination 264 

Kerosene  lamp 128 

Kirchhoff's  law  of  radiation 85 

Lamps,  arc 151 

Light  flux . .  177, 186, 256, 259 


INDEX.  297 

PAGE 

Light  flux,  combination  by  addition 285 

comparison  of  radiators 197 

density 177,  256,  259 

distribution  by  frosted  globe 223 

distribution  by  opal  globe 223 

as  germicide 60 

intensity 177, 186 

measurement 166 

Lightning  phenomena  frequency  and  wave  length 17 

Light  not  a  vector  quantity 284 

as  physiological  effect 168 

production  by  incandescence 74 

also  see  Radiation. 

sources,   comparison 202,  209, 215 

and  enclosing  globe,  comparison 224 

intensity 256,  259 

as  transversal  vibration 8 

Lighting,  tower 274 

Light  unit 177 

as  wave  motion 6 

Lime  light 136 

Limits  of  electrical  waves,  frequency  and  wave  length 17 

frequency  of  electric  waves 16 

Linear  radiator  shaded  by  circular  flame 210 

Line  spectrum 26 

of  arc 118 

Local  or  concentrated  illumination 269 

illumination 226, 260 

and  uniform  illumination 264 

Logarithmic  scale  of  frequency 14 

law  of  sensation 38 

Long  burning  carbon  arc 160 

Longitudinal  vibration 7 

Lumen 186 

as  unit  of  light  flux 257 

Luminescence 94 

of  arc 117 

chemical 97 

of  flame 133 

by  heat 91 

Luminometer 43, 174 

chart 175 

Luminous  arc 123, 160 

distribution 210,  215,  220 

efficiency 149 

lamp 157 

radiator 195 


298  INDEX. 

PAGK 

Luminous  arc  in  street  illumination 240 

flame 129 

Magnesium  flame 134 

Magnetite  arc 123 

constants 140 

distribution 220 

in  street  lighting 236, 240 

Magnetite  arc  as  typical  arc 109 

Massed  and  distributed  illumination 269 

Maximum  candle  power 184 

visibility 46 

Mean  spherical  intensity 180, 184, 257 

Measurement  of  light  and  radiation 166 

Mechanical  equivalent  of  light 42 

Mechanism  of  arc  lamp . 152 

Melting  points  of  elements 77 

Mercury  arc,  constants 140, 145 

greenish  blue 123 

higher  frequency  of  ultra-violet  light 13 

rectification 117 

rectifier 114 

rectifier  system 165 

tube  as  radiator 195 

Meridian  curve  of  light 180, 188 

Metal  arcs  and  ultra-violet  light 56 

unsteadiness 125 

Metallic  carbon 81 

Metals  as  most  opaque  bodies 31 

Methane 128 

Mica  opaque  for  ultra-violet  light 13 

Micron 7 

Micro-organisms,  effect  of  light 61 

Milk  glass  globe  diffusion 221 

Minimum  visible  amount  of  light 45 

Mirror 28 

reflector  and  light  distribution 215 

Misleading  character  of  meridian  curves  of  light 188 

polar  curves  of  light 187 

Modifications  of  carbons 81 

Negative  carbon  electrode  shadow 203 

spot  of  arc 107, 110, 125 

terminal,  also  see  Cathode. 

determining  character  of  arc 108 

Newton's  theory  of  radiation 4 

Normal  temperature  radiation 75, 84 


INDEX.  299 

PAGE 

Objects,  effect  on  light  distribution 283 

Objective  or  actual  color 33 

color  in  illumination 265 

illumination 261 

Observer,  effect  on  light  distribution 283 

Octave  as  frequency  scale 14 

Oil  lamp 128 

Opal  globe 262 

diffusion 22 1 

and  nature  of  shadow 268 

Opaque 32 

body 31 

colors 32,  36 

Open  arcs,  efficiency 148 

Open  carbon  arc 160 

Oscillations,  electrical,  frequency  and  wave  length 17 

Osmium  lamp 79 

Overlap  of  light  fluxes  in  illumination 267 

Oxygen  in  flame 132 

Ozone  production  by  ultra-violet  light 64 

Paraffine  candle 131 

photometer 171 

Parallelogram  law  and  light  flux 284 

Pathogenic  bacilli,  effect  of  light 61 

Pathological  effects  of  radiation 57 

Pentane  lamp 178 

Periodic  system  of  elements  and  radiation  efficiency 77 

Permeability  and  refractive  index 24 

Personal  equation  of  user  in  illuminating  engineering 287 

Physical  phosphorescence 95 

Physiological  effect  of  sensation 40 

in  light  measurement 167 

measure  of  light 168,  186 

problems  of  illumination 262 

illuminating  engineering 277 

unit  of  light 177 

Phosphorescence 66,  94 

Photography 63 

Photometry 169 

Phototheraphy 61 

Pigment  in  acclimatization 59 

Plane  illumination 286 

as  radiator 190 

Plants,  action  of  light 64 

Point  as  radiator 189 

Polar  curves  of  light  distribution 187 


300  INDEX. 

PAGE 

Polarized  wave 8 

Positive  terminal  of  arc 109 

also  see  Anode. 

Power  burn 53 

effect  of  radiation 57 

Primary  standard  color 179 

standards  of  light 177 

Prismatic  reflection  and  refraction 221, 224 

Problems  of  illumination 260 

Protection  against  ultra-violet  light 55 

Protective  device  of  arc  lamp 151 

mechanism  of  the  eye  against  radiation 50 

Protoplasm,  effect  of  radiation 57 

Pulsations  of  arc  voltage 159 

Pupil  contraction 262 

Putrefactive  bacilli,  effect  of  light 60 

Pyro-luminescence 96 

Pyrometers,  visual 90 

Quality  or  color  of  light 269 

Quartz  as  most  transparent  body 31 

transparent  for  ultra-violet  light 13 

Radiant  heat 1 

Radiation  efficiency 86 

as  a  form  of  energy 1 

measurement 166 

measured  as  power 166 

power 72 

also  see  Light. 

Radiators,  comparison 202, 209 

of  light 187 

separate  from  flame 135 

Radio-active  substances 14 

Radio-fluorescence 95 

Radio-luminescence 95 

Radio-phosphorescence 95 

Radio-therapy 61 

Radium  rays,  harmful  effects  of 58 

Range  of  frequencies  of  radiation 17 

Reading  distances  measuring  light 174 

Rectification  by  arcs 114 

Rectifying  range  of  arc  voltage 116 

Red  fluorescence 67 

light,  chemical  action  of 64 

therapeutic  effect 62 

lines  of  mercury  arc  spectrum 120 


INDEX.  301 

PAGE 

Red  mercury  arc 121 

Reduction  factor  of  incandescent  lamp 182 

Reflected  light  from  walls  and  ceiling,  calculation 250 

Reflection  affecting  light  distribution 212 

of  light  by  body 28 

regular,  and  light  distribution 215 

and  shadow  with  radiator 219 

Reflectors,  comparison 215 

as  secondary  radiators 212 

as  virtual  radiators 215 

Refraction  law 23 

and  light  distribution 221 

spectroscope 25 

Refractive  index 23 

and  dielectric  constant 24 

and  permeability 24 

Regenerative  flame  lamp 126 

Regular  reflection 28, 215 

and  refraction 224 

Regulator  of  arc  machine 164 

Reversed  spectrum 27 

Ring  carbon 82 

Room  illumination,  calculation 247 

by  incandescent  lamp 242 

Rounded  circular  surface  as  radiator 193 

Sand  blasted  globe,  diffraction 221 

Saprophytic  bacilli,  effect  of  light 60 

Searchlight  beam,  intensity 234 

Secondary  radiator  and  reflector 212,  216 

Selective  radiation 87 

Sensitivity  curve  of  the  eye 43,  47 

Sensitivity  of  the  eye 263 

and  frequency 40 

to  ultra-violet  light 54 

maximum,  of  the  eye 46 

Separate  radiator  of  flame 135 

Series  arc  lamp 157 

system  of  arc  lighting 162 

Shadow 202 

blurring  of,  in  illumination 268 

of  diffused  light 280 

in  illuminating  engineering 266 

of  negative  carbon 203 

of  negative  terminal  of  arc 148 

number  of 268 

proper  intensity  in  illumination 266 


302  INDEX. 

PAGE 

Shadow  photometer 171 

in  street  lighting,  defective 273 

theory  of 269 

Shell  of  arc  flame 110 

Short  burning  carbon  arc 160 

Short  ultra-violet  light,  destructive  effect 52 

Spherical  intensity 257 

Signal  lights,  color 98 

Silicides  as  refractory  bodies 78 

Single  loop  filament,  distribution  curve 199 

Smokiness  of  flame 130 

Smoky  flame 129 

Sound  as  longitudinal  vibration 8 

waves,  frequency  and  wave  length 17 

Spark  voltage 100 

Specific  effects  of  high  frequency  radiation 51 

Spectrum  of  arc 118 

and  negative  terminal 108 

by  diffraction 26 

of  flames ,  .  134 

of  luminescence 96 

of  radiation 17 

by  refraction 25 

Sphere,  illumination 287 

as  radiator 189 

Spherical  intensity 180 

reduction  factor  of  incandescent  lamp 182 

Stability  curve  of  the  arc 142, 144 

limit  of  arc 143 

Stable  branch  of  arc  characteristic 142 

Standard  candle 170 

Starting  of  arc   106 

by  auxiliary  arc 112 

device  of  arc  lamp 151 

Steadying  device  of  arc  lamp 151 

reactance  or  resistance  of  arc  lamp 151 

Stephan's  law 70,  75 

Stimulating  effect  of  radiation 57,  59 

Straight  line  as  radiator 195 

Street  illmination  by  arcs 234 

comparison  of  arc  lamps 240 

Street  lighting 226,  272 

calculation 238 

comparison  of  illuminants 236 

defects 273 

Striated  Geissler  discharge 101 

Subjective  or  apparent  color 34 


INDEX.  303 

PAGE 

Subjective  color,  control  in  illumination 265 

illumination 262 

Sulphur  flame 135 

Sunburn 59 

Sun  spectrum 27 

Surges,  electrical,  frequency  and  wave  length 17 

Symptoms  of  ultra-violet  burns 54 

Synthetic  action  of  plants 65 

Table  illumination 253 

Tanning 59 

Tantalum  lamp 80 

Temperature  of  arc  stream 108 

of  carbon  filament 79 

and  frequency  of  radiation 73 

of  maximum  efficiency  of  light  production 74 

measurement  by  radiation  law 89 

radiation   70 

of  flame 128 

law  of 84 

standard 178 

Therapeutic  use  of  light 61 

effects  of  radiation 57 

Thermo-couple  measuring  radiation  power 166 

Thermo-luminescence 95 

Threshold  value  of  visibility 45 

Titanides  as  refractory  bodies 78 

Titanium  arc,  white 123 

carbide  arcs 117, 123 

Total  illumination    226, 287 

of  room 253 

Tower  lighting 274 

Transfer  of  arc  between  anodes 112 

Transient  electric  phenomena   18 

Translucent  body 31 

Transmission  of  light  by  body 28 

Transparent 32 

body 31 

color 31, 32,  36 

Transversal  vibration 7 

Tungsten  lamp 80 

as  refractory  element 78 

Also  see  Wolfram. 

Typical  arc 109 

Ultra-red  rays 12 

frequency  and  wave  length 14, 17 


304  INDEX. 

PAGE 

Ultra-violet  arc  lamp 12 

burn 53 

burn  in  wireless  telegraphy 54 

iron  arc 119 

lamp 135 

light  of  arc 55 

light  and  fluorescence 67 

light  harmful  effect 62 

therapeutic  action 61 

radiation,  frequency 14 

rays 12 

frequency  and  wave  length 17 

Unidirectional  conduction  of  electric  arc 113 

Uniform  distribution  illumination  curve 229 

or  general  illumination 269 

illumination 226,  260 

in  street  lighting 235 

Uniformity  in  street  lighting 272 

Uniform  and  local  illumination 264 

total  illumination 228 

Unit  of  light 177 

Unstable  branch  of  arc  characteristic 142 

Unsteadiness  of  jaetal  arcs 125 

Vacuum  arc 145 

Vapor  pressure  of  the  arc 105 

stream  of  the  arc 105 

tension  of  carbon 79 

Vector  quantities  and  light 284 

Velocity  of  electrical  radiation 4 

light 2 

in  a  medium 23 

Vertical  illumination 227 

Violet  light,  harmful  effect 52 

specific  effect 52 

Violle  standard  of  light 177 

Virtual  radiator 221 

and  reflector 216 

Visible  light,  frequency  and  wave  length 17 

radiation 10 

power  measurement 168 

range .  „ 14 

and  temperature 74 

Visibility  range  of  radiation 37 

Visual  pyrometers 90 

Walls,  albedo 246 

Warm  light 48 


INDEX.  305 

PAGE 

Waste  of  light  flux  by  absorption 261 

Water  as  transparent  body 31 

Wave  length  determination 6 

of  visible  radiation 10 

Welsbach  mantle 92, 136 

White 32 

body 29 

iron  arc 1 19 

Whiteness  or  albedo 30 

Willemite  fluorescence 13 

Wireless  telegraph  waves,  frequency  and  wave  length 15,  17 

ultra-violet  burn 54 

Wolfram  as  refractory  element 77 

also  see  Tungsten. 

X-ray  frequency  and  wave  length 14, 17 

harmful  effects  of 58 

specific  action 56 

Zinc  arc,  constants 140 

rectification.  .  117 


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